When art works fetch spectacular auction prices, like the record $450.3 million for Leonardo da Vinci’s “Salvator Mundi” in 2017, the world’s focus turns for a moment to the arcane goings-on of the international art trade. But with the market in a downturn for the last two years, there have been few attention-grabbing sales at the world’s two biggest and oldest auction houses, Sotheby’s and Christie’s.

An exception came at November’s marquee auctions of modern and contemporary art in New York, when the world’s media — and social media in particular — were momentarily enthralled by the seeming absurdity of a cryptocurrency investor spending $6.2 million at Sotheby’s for a duct-taped banana. But there is a big difference between $6.2 million and $450.3 million.

Sales at Sotheby’s and Christie’s were down for the second year in a row in 2024, according to preliminary figures released by the companies in December. With both supply and demand for big-ticket art in a slump, the auction houses are making major bets on selling luxury goods and niche experiences to make up the shortfall.

Sotheby’s estimated it would have turned over about $6 billion in auction and private sales by year-end, a decline of 24 percent on 2023. Christie’s announced projected aggregate sales of $5.7 billion, down 6 percent year-on-year. Back in 2022, Sotheby’s and Christie’s posted annual turnover of $8 billion and $8.4 billion.

“The auction houses have major problems,” said Christine Bourron, the chief executive of the London-based company Pi-eX, which analyzes art sale results. “They really need to do some thinking about how they can bring some life into their auction business. People who have an interest in art want to have an experience,” added Bourron, who, like many followers of the auction market, finds both Sotheby’s and Christie’s live and online sales increasingly predictable.

Sotheby’s is owned by the French-Israeli telecoms magnate Patrick Drahi, whose beleaguered Altice group is burdened with $60 billion of debt. Sotheby’s deteriorating performance led the auction house to reach out to Abu Dhabi’s sovereign wealth fund, A.D.Q., for a $1 billion cash-for-equity bailout and to lay off more than 100 employees in December. This followed some costly infrastructure decisions: Sotheby’s $100-million purchase of the Breuer Building in New York’s Madison Avenue, the opening of a new headquarters in Paris and the development of a futuristic exhibition and retail space in Hong Kong.

Sotheby’s website now abounds with opportunities to buy pre-owned luxury items at auction or by “instant purchase,” as if in a store, ranging from real estate, classic cars and dinosaur fossils, to smaller prestige collectibles like designer handbags, jewelry, fine wines and game-worn N.B.A. jerseys.

Josh Pullan, Sotheby’s global head of luxury, said sales of such goods draw in wealthy clients who may, in time, start to buy high-end art. “Luxury categories are for us a vital gateway for new, often younger, collectors,” he added.

Last year, luxury generated about 33 percent of sales at Sotheby’s, compared with 16 percent at Christie’s, according to the companies’ communications teams. But the category attracted more buyers than art did.

Guillaume Cerutti, the chief executive of Christie’s, spoke to reporters last month during an end-of-year media call. “Luxury has an advantage, because of the model and the price points,” he said. “Luxury and art will merge with each other,” he added, hinting at future synergies of presentation and categorization.

Christie’s is owned by the luxury goods billionaire François-Henri Pinault, whose Kering conglomerate has also been hit by flagging sales. After introducing handbag auctions back in 2014, Christie’s is now having to catch up with Sotheby’s offering of luxury items and trophy collectibles, like dinosaur skeletons. In September, Christie’s announced that it had reached an agreement to acquire the California-based classic car auctioneers Gooding & Co., setting up a rivalry with Sotheby’s car business, RM Sotheby’s, which last year turned over $887 million in classic auto sales.

“The luxury resale market presents a compelling opportunity for auction houses,” said Daniel Langer, a professor of luxury strategy at Pepperdine University in Malibu, Calif. “Storytelling is a critical success factor in the luxury industry. Auction houses excel in this area — take the recent banana auction as an example,” he added. Sotheby’s marketing, like that of a luxury brand, had skilfully woven a narrative around the sensation that the banana sculpture, by the Italian artist Maurizio Cattelan, created when first exhibited at the Art Basel Miami Beach fair in 2019.

However, this opportunity comes with “significant challenges,” according to Langer. He pointed out that unlike luxury brands, auction houses don’t produce and price all of their own inventory; profit margins on new luxury items are often much higher than their resold equivalents; and unlike conglomerates such as LVMH and Kering, auction houses can’t scale their transactions through a network of retail outlets. These disparities between retail and resale “could limit the overall financial impact of luxury for auction houses,” he said.

Changing spending patterns among the wealthy could also affect demand.

Global sales of luxury flatlined in 2024 for the first time since 2008 (excluding 2020, during the coronavirus pandemic), according to a recent report by the management consultants Bain & Co. The report’s authors said consumers were prioritizing “experiences over products” in these uncertain times and that the luxury goods market, rather like the art market, is suffering from buyer fatigue.

“The super-wealthy in their 30s, 40s and 50s are spending their money on luxury experiences,” said Doug Woodham, a former Christie’s executive who now advises on art-related finance. “That’s money that isn’t being spent on a Matisse drawing,” he added.

“With superluxury experiences, the social cache is so much higher,” said Woodham, who pioneered handbag sales at Christie’s in 2014. “For half a million dollars I can have my 10 best friends on a lavish yacht. They will remember that more than sitting in my house with a Rothko on the wall.”

The global luxury yacht charter market grew to an all-time high of $16.3 billion in 2024, a 6 percent increase on the previous year, according to the Business Research Company. It said that growth has been driven by the popularity of “exclusive and exotic travel destinations” and the “ongoing trend towards experiential luxury.”

In September, Sotheby’s collaborated with the Marriott International hotel chain and the fashion house Alexander McQueen to offer a sealed bid auction, in which bidders can’t see the rival offers. The winner got a two-night stay one of the group’s 5-star London sites as part of an experience that the Sotheby’s website said would “transport guests to where a teenaged McQueen first learned the art of tailoring.” Also included were a five-course fine-dining meal for two, a bespoke tour of London with a private visit to the Victoria & Albert Museum and a personalized photo session with Ann Ray, a longtime McQueen collaborator. Classifying the auction as a private sale, Sotheby’s declined to reveal how much the winning bidder paid for this unique luxury experience, but the presale estimate was $12,000 to $18,000.

Could selling memories, instead of art, be the future of the auction business?

Republicans are preparing to cut taxes, slash spending and slow immigration in a broad agenda that will require unifying an unruly party behind dozens of complicated policy choices.

For now, though, they are struggling with a more prosaic decision: whether to cram their policy goals into one bill or split them into two.

It is a seemingly technical question that reveals a fundamental divide among Republicans about whether to prioritize a wide-ranging crackdown on immigration or cutting taxes, previewing what could be months of intramural policy debate.

Some Republicans have argued that they should pass two bills in order to quickly push through legislation focused on immigration at the southern border, a key campaign promise for Mr. Trump and his party’s candidates. But Republicans devoted to lowering taxes have pressed for one mammoth bill to ensure that tax cuts are not left on the cutting-room floor.

President-elect Donald J. Trump met with Republican senators in Washington on Wednesday, as those lawmakers sought clarity on his preferred strategy. He has waffled between the two ideas, prolonging the dispute.

“Whether it’s one bill or two bills, it’s going to get done,” Mr. Trump told reporters after the meeting.

Republicans are planning to ram the partisan fiscal package through the Senate over the opposition of Democrats using a process called reconciliation, which allows them to steer clear of a filibuster and pass bills with a simple majority vote. But for much of this year, Republicans will be working with a one-seat majority in the House and a three-seat majority in the Senate, meaning they will need near unanimity to pass major legislation.

That has left some worried that it will be hard enough passing one bill, much less two.

“There’s serious risk in having multiple bills that have to pass to get your agenda through,” Representative Steve Scalise of Louisiana, the majority leader, said. “When you know you’ve got a lot of people that want this first package, if you only put certain things in the first package, they can vote no on the second and you lose the whole second package. That would be devastating.”

Adding to the urgency of achieving their policy goals, Republicans are facing a political disaster should they fail to deliver. Many of the tax cuts they put into place in 2017, the last time Mr. Trump was president, expire at the end of the year. That means that taxes on most Americans could go up if Congress does not pass a tax bill this year.

Passing tax cuts can take time, though. While much of the Republican tax agenda involves continuing measures the party passed in 2017, Mr. Trump and other Republicans have floated additional ideas, including no taxes on tips and new incentives for corporations to manufacture in the United States. Ideas like that could take months to formulate into workable policy.

Then there is the gigantic cost. The nonpartisan Congressional Budget Office estimates that simply extending the 2017 tax cuts would cost more than $4 trillion over a decade — a price tag that would grow if other tax cuts, like Mr. Trump’s proposal to not tax overtime pay, are included.

Further complicating support for the legislation is that Republicans plan to raise the debt limit through reconciliation, another sensitive issue for fiscal hawks.

Members of the ultraconservative House Freedom Caucus have said they would not support any legislation unless the costs it introduces are offset by spending cuts. While most Republicans support reining in federal spending, agreeing on which federal programs to slash always proves harder than expected. In an attempted workaround, Republicans have instead begun to explore ways to change Washington’s budget rules so the tax cuts are shown to cost less.

The complexity of pulling together a tax bill that can secure the necessary votes has some Republicans hoping to hold off until later in the year and first charge ahead with a smaller bill focused on immigration, energy and military issues. Republicans have not yet publicly sketched out what that bill would look like.

Proponents of that strategy argue it would deliver Mr. Trump an early political victory on immigration and treat a top Republican campaign issue with the urgency it deserves.

“The No. 1 priority is securing our border,” Representative Byron Donalds of Florida told reporters on Tuesday. “In my opinion it’s the top priority, and everything else is a close second.”

Senator Lindsey Graham of South Carolina, the chairman of the Budget Committee who will be overseeing the reconciliation process, has also pressed for a two-bill approach. “If you hold border security hostage to get tax cuts, you’re playing Russian roulette with our national security,” he said.

Republicans have looked to Mr. Trump to intervene and set a clear direction for the party. On Sunday, he wrote on social media that Congress should pass “one powerful Bill,” an apparent victory for lawmakers like Representative Jason Smith of Missouri, the chairman of the House Ways and Means Committee, who had championed that approach. Mr. Trump’s equivocation since then, though, has left Republicans still unsure of which strategy they should pursue.

Mr. Trump’s meeting with top Republican senators on Wednesday will be followed by a discussion with various House Republicans in Florida over the weekend.

In a sign of how politically complicated the tax cut discussion could get, one of the sessions is expected to focus on relaxing the $10,000 limit on the state and local tax deduction, known as SALT.

Republicans included the $10,000 limit in the 2017 tax law as a way to contain the cost of that legislation. But the move angered House Republicans from high-tax states like New York and New Jersey, many of whom voted against the entire 2017 tax bill as a result. Such defections are a luxury that Republican leaders can’t afford this year given their narrow majority.

G.O.P. lawmakers from New York, New Jersey and California could tank a tax bill if they are unsatisfied with how the provision is handled. They are now pushing to lift the cap as part of the party’s tax bill. Eliminating the cap entirely could add roughly $1 trillion to the price tag of the legislation.

Maneuvering ambitious policy agendas through Congress has often been a messy and time-consuming process for presidents. A Republican effort to repeal the Affordable Care Act during Mr. Trump’s first term collapsed after more than six months of discussion.

After quickly passing pandemic relief measures in 2021 under President Biden, much of Democrats’ broader agenda was stymied for almost two years before a second party-line measure passed that was far narrower than many in the party had hoped.

This time around, Republicans will be grappling not only with a historically slim margin in the House, but also a president prone to sudden changes of heart.

“You can argue the merits of both” strategies, said Representative Jodey Arrington, a Texas Republican who leads the House Budget Committee. “He has to tell us what he wants and what he needs.”