On the day Barack Obama took over the White House on Jan. 20, 2009, six of his cabinet nominees were immediately confirmed by the Senate. He signed his first piece of legislation — a major bill guaranteeing equal pay for women — into law just nine days later.

Should Vice President Kamala Harris win the presidency, she could not count on such cooperation from the chamber where she, like Mr. Obama, once served. Mr. Obama benefited from a big Democratic majority in the Senate. But Democrats are in control now by only the slimmest of margins, and their chances of keeping that majority most likely hang on the fate of Senator Jon Tester of Montana, who is currently trailing in his re-election race in his solidly red state.

If he should lose and Democrats fail to score any upsets in a handful of races they are not favored to win, Republicans would take over the Senate, putting Ms. Harris at loggerheads from the start with a newly empowered G.O.P. bent on stymying her at every turn.

“It is night and day,” Senator Richard Blumenthal, Democrat of Connecticut, said about the difference between his party hanging on and Republicans winning the Senate. “It’s loss of control, putting the agenda very much in peril.”

At the moment, most analysts lean toward Republicans capturing the Senate, given a political map that was stacked against Democrats from the start and has only gotten tougher for them. The G.O.P. is all but certain to win the West Virginia seat being vacated by Senator Joe Manchin III. And Mr. Tester is lagging in a state expected to vote overwhelmingly for former President Donald J. Trump.

The swing of those two seats alone would be enough to knock Democrats out of their 51-to-49 majority and fundamentally alter the governing landscape if they cannot secure an upset win elsewhere. Polls show that other Democratic incumbents in battleground states, including Sherrod Brown in Ohio and Jacky Rosen in Nevada, continue to run ahead of their Republican opponents.

The prospect of a new Democratic president and a Republican Senate is a rare scenario. The winner of the White House historically has had coattails that brought Congress into line — at least at the start. Presidents of both parties elected in recent decades have consistently been sworn in with their allies controlling both the House and the Senate. Not since Grover Cleveland in 1884 has a Democrat been elected to a first presidential term with a Republican Senate.

The potential for winning the White House and losing the Senate is a chief reason that Democrats are so determined to re-elect Mr. Tester, promising to stick with him to the finish whatever the polls say. Democrats say they have confidence that Mr. Tester can pull out a victory.

“There’s no world that you can conceive of that I’m not going to be in Montana until the end,” Senator Gary Peters, Democrat of Michigan and the chairman of the party’s Senate campaign operation, said during a recent speech at the National Press Club. “Jon Tester will have everything he needs to win.”

Yet Democrats are also beginning to allocate resources to the Republican-dominated states of Texas and Florida, where Senators Ted Cruz and Rick Scott have shown some weakness, as alternative paths to a Senate majority should Mr. Tester be unable to prevail. And in a surprise, Dan Osborn, an independent, is mounting a strong bid against Senator Deb Fischer, a Republican, in Nebraska. An upset there could deny Republicans a majority.

The stakes are enormous, particularly since the old notion of a honeymoon for a newly elected president is out the window. These days, many voters from the losing party expect their representatives to put up a fight, not rally around the winner.

Should they lose their Senate majority, Democrats would give up their all-important committee chairmanships. With Republicans in control, Ms. Harris would have to think about her cabinet choices in an entirely different way. The idea that presidents are entitled to their chosen nominees is a quaint one these days, and any picks would have to pass intense G.O.P. scrutiny.

Instead of making selections that could pass muster with a Democratic majority, Ms. Harris would need to choose candidates who could appeal to enough Republicans to win confirmation should they even clear committee and reach the floor for a vote. There would be no flurry of approvals on her first day in office.

“Obviously we would be in a position to negotiate nominations from everything from the Supreme Court to the Department of Homeland Security and everything in between,” said Senator John Cornyn, Republican of Texas and one of the men vying to replace Senator Mitch McConnell of Kentucky as party leader beginning in 2025. “It will be a different role.”

Mr. Cornyn also noted that a Republican Senate would be able to block Democrats from gutting the filibuster to pass new nationwide protections for abortion rights, a move that Ms. Harris has said she would support.

Things could get even more difficult when it comes to lifetime appointments to the federal courts. Democrats have so far placed 213 judges on the bench during the Biden administration. Republicans would want to slow that momentum and screen Ms. Harris’s choices extremely carefully after the confirmations of scores of judges they opposed.

As for the Supreme Court, it is not certain that a Democratic president could even get a nominee through a Republican-controlled Senate should a vacancy occur. At minimum, any Supreme Court nominee would need to be much more centrist than the person a Democratic president might select if her own party held the Senate majority.

“Particularly with the judiciary, because we have the power of confirmation, I think they’re going to have to think long and hard about who they submit and whether or not they think they could get them cleared through the Senate,” said Senator John Thune, Republican of South Dakota and another candidate for party leader. “But that’s a bridge we’ll cross if and when we come to it. Certainly we’re hoping we have all the reins of power next year.”

Depending on the final Senate margin, having Ms. Harris in the White House and the G.O.P. controlling the Senate could empower the dwindling band of more moderate Republicans like Senators Susan Collins of Maine and Lisa Murkowski of Alaska, who might team up with Democrats on select issues and be persuaded to back some Democratic nominees. They would still have to find ways to force legislation to the floor and overcome the 60-vote filibuster.

Of course, a Democratic White House and a Republican Senate is just one possible scenario from the election, and nothing is locked in at this point. But a Trump presidency and a Democratic Senate seems a far more unlikely outcome while both parties still have a chance at securing the coveted trifecta of controlling the House, the Senate and the White House.

Under virtually any predicted outcome of the voting in November, the partisan margins in both the House and the Senate are going to be tight as they have been the past two years, making legislating precarious.

Democrats say they have shown they can make progress in a divided Congress by striking spending and legislative deals with Republicans while advancing executive branch and judicial nominees. They would relish a chance to do so again — but they would need to hang on in the Senate.

“Over the last four years,” said Senator Chuck Schumer, Democrat of New York and the majority leader, “we have shown what can get done with a Democratic president and a Democratic majority in the Senate.”