Two states nearly a thousand miles apart will on Tuesday provide the best evidence yet of whether President Trump and his Republican allies maintain robust support or whether they face a growing backlash led by a re-energized Democratic Party.

In Wisconsin, a nearly $100 million race for control of the State Supreme Court has morphed from an important clash over the state’s direction into a referendum on Elon Musk’s supersized role in national politics.

In Florida, one of two special elections for deep-red House seats suddenly seems too close for comfort for Republicans. Democrats, while still expecting to lose, are watching the margins closely for signs that their party is ascendant.

Here are five big questions heading into Tuesday’s elections.

Will Elon Musk’s millions pay off?

Mr. Musk’s support for Brad Schimel, the conservative candidate in Wisconsin, has been a full-service political operation.

The billionaire and groups tied to him have spent more than $25 million, financing a potent ground game. An army of $25-an-hour canvassers has knocked on Trump voters’ doors, and pallets of glossy mailers have assured Republicans that Judge Schimel is a Trump ally. A conservative nonprofit with ties to Mr. Musk has helped blanket the airwaves with ads bashing the liberal candidate, Susan Crawford, as weak on crime. And Mr. Musk’s giving includes $3 million to the Republican Party of Wisconsin, which has funneled the money to help Judge Schimel.

That was all before Mr. Musk spoke for nearly two hours at a rally for Judge Schimel on Sunday night in Green Bay.

If Mr. Musk’s extraordinary effort is successful, Wisconsin Republicans will be hopeful of friendly rulings by a conservative-controlled court on cases about abortion rights, voting access and the power of the state’s Republican-run Legislature.

It is possible, however, that Mr. Musk’s largess comes at a political cost to Judge Schimel. Polling shows that Mr. Musk is just as unpopular among Wisconsin Democrats as Mr. Trump is, but without as much residual loyalty from Republicans. Democrats have framed Judge Crawford’s campaign around the idea that she is battling the world’s wealthiest person.

“We are in uncharted territory where we now have the richest man in the world who is trying to buy our election and the question is: Can he do it?” said Sarah Godlewski, the Democratic secretary of state of Wisconsin.

At her closing campaign rally Monday night in Madison, Judge Crawford skewered Mr. Musk for appearing at his rally wearing the foam yellow headwear preferred by the state’s sports fans.

“Let me talk about my opponent, Elon Musk,” she said. “I saw a picture of him yesterday with a cheesehead on. First time he’s been in Wisconsin, he has not earned the right to wear a cheesehead.”

Is the Democratic energy finally here?

Democratic hopes have slowly, cautiously started to rise.

The party crowed about flipping Republican-held state legislative seats in recent special elections in Iowa and Pennsylvania. And on Saturday, voters in Louisiana rejected four proposed constitutional amendments backed by Gov. Jeff Landry, a Republican, that would have overhauled parts of the state’s tax codes and toughened penalties for juvenile offenders.

But none of those was nearly as expensive or prominent as Tuesday’s contests, and so the question of whether they were one-off upsets or a harbinger of a broader Democratic resurgence will be determined by what happens in Wisconsin and, to a lesser extent, Florida.

A victory by Judge Crawford, a mild-mannered jurist, could put wind in the sails of a new Trump resistance, similar to Jon Ossoff in April 2017. While Mr. Ossoff, now a Georgia senator, lost what was then the most expensive House race ever, he became a fund-raising juggernaut and demonstrated to scores of other candidates a path to viability against Republicans in the first Trump era.

Wisconsin Democrats have placed Mr. Musk at the center of their messaging operations in the race: To make sure voters got the point, they branded a statewide tour “The People v. Elon Musk.” Fearful of being drowned out by Mr. Musk’s millions, Democrats have helped Judge Crawford shatter fund-raising records.

“We are figuring out the path forward,” said State Representative Greta Neubauer, a Racine Democrat who is her chamber’s minority leader.

Are Democrats really competitive in Florida?

House Republicans had expected their razor-thin majority to grow easily by two seats on Tuesday in elections to replace congressmen Mr. Trump picked last year to join his cabinet.

One, Michael Waltz, became the national security adviser, while the second, Matt Gaetz, resigned his seat and later withdrew from consideration as attorney general amid an ethics investigation and Republican opposition.

Mr. Trump endorsed Jimmy Patronis, the state’s chief financial officer, to replace Mr. Gaetz in the Panhandle and State Senator Randy Fine to replace Mr. Waltz in a northeastern district that includes the NASCAR hub of Daytona Beach.

But Mr. Fine’s Democratic opponent, Josh Weil, has handily out-raised him, prompting public warnings about Mr. Fine’s chances of a comfortable victory in a district Mr. Trump won by 30 percentage points. While Republicans are still expected to prevail, both parties are watching the margin of victory closely.

Despite the Republican worries, Democrats have not made significant outside investments to help Mr. Weil’s campaign. But on Friday, Mr. Weil did score a notable national endorsement from Senator Bernie Sanders, the Vermont independent, and he campaigned on Sunday with Ken Martin, the chairman of the Democratic National Committee.

The last race for the Wisconsin Supreme Court, two years ago, cost about $56 million to became the most expensive judicial election in American history.

That election drew 1.8 million voters, or about 56 percent of the state’s turnout in the presidential election in 2020 — a high percentage for a state court race.

Now, with spending approaching $100 million, a key factor in the outcome is how much higher turnout will go.

America Votes, a Democratic voter mobilization group that is active in the state, estimates that just over two million Wisconsinites will vote, an increase that could account for either juiced Democratic interest or a successful Republican turnout operation by Mr. Musk. If that many Wisconsinites do vote, the turnout will be about 60 percent of the state’s turnout last November.

And as much as voters say they hate onslaughts of negative advertising and attack mailers, the evidence shows that they drive up interest, excitement and turnout.

“Everywhere I’ve been in the state, we’re getting crowds like we did last November,” said Brian Schimming, the chairman of the Republican Party of Wisconsin. “People are clicked in.”

Is Musk the future of our elections?

Mr. Musk has nearly unlimited wealth, the president’s ear and far-ranging power in Washington.

If he can single-handedly alter a state judicial race, how else might he inject himself into the country’s elections?

Victory in Wisconsin could embolden Mr. Musk to grow even more aggressive in throwing his billions behind Republican candidates for office this year and in the 2026 midterm elections. That could leave conservative candidates even more in thrall to Mr. Trump, if their primary financial benefactor continues to work out of the White House.

This is all happening while Mr. Musk stands to benefit financially from the candidates he has thrown his money and influence behind. Tesla, the electric vehicle company Mr. Musk controls, has a case against Wisconsin pending in the state’s courts, and Mr. Trump has gone out of his way to promote the billionaire’s products from the White House.

Defeat for conservatives, of course, would hardly mean that Mr. Musk would stop spending on elections. But it would prove to Democrats that he is beatable with enough money and base energy.

Still, while Democrats may see Mr. Musk as a figure who fires up their base and supercharges liberal fund-raising, that is a lot easier for them to do when Wisconsin is the marquee race in the country and a focus of national attention.

If Mr. Musk were bankrolling dozens of Trump-allied candidates for governor, Senate and Congress across the country next year, it could be a far more difficult proposition to match his financial might with the same degree of grass-roots enthusiasm when national attention is more diffuse.