President Trump hit a record-high approval rating in one of the country’s most influential polls Monday, as Democrats lost support for impeachment over the past six weeks of hearings.

Impeachment has cost Democrats their first House seat as well. Rep. Jefferson Van Drew of New Jersey, an outspoken critic of the process, fled the Democratic Party to join the Republicans.

Democratic leaders aren’t changing course, though.

They plan to push two articles of impeachment through the House Rules Committee on Tuesday and set up a final floor vote Wednesday. Approval is all but assured, which would make Mr. Trump only the third president in history — though the second in the past quarter-century — to be impeached.

Democrats hoped the move would win over voters, but their case has fallen flat.

The Quinnipiac University Poll found a majority, 51%, oppose impeachment and removal of the president, and 45% say Mr. Trump should be ousted.

Those numbers are worse for Democrats than they were in late October, before the House held weeks of hearings that they said would show the president had committed impeachable crimes.

An NPR/PBS NewsHour/Marist poll also released Monday found more opponents than supporters of impeachment, though the margin was tighter at 48% to 47%.

“It’s like the hearings have never happened,” said Lee Miringoff, director of the Marist Institute for Public Opinion. “The arguments have only served to reinforce existing views, and everyone is rooting for their side.”

That is bad news for Democrats, who insisted they would act only if they had clearly made the case for impeachment and earned bipartisan support. Instead, they are likely to face unified Republican opposition and may be the ones who end up divided.

Mr. Trump, meanwhile, got more good news out of Quinnipiac. Pollsters said his approval rating hit 43% — tied for a record high in their survey. Americans are also more enthusiastic about the economy than they have been in 18 years, Quinnipiac said.

“That view of a strong economy seems to be helping President Trump match his highest job approval rating since being elected, despite facing becoming the third president in U.S. history to be impeached this week,” said Mary Snow, an analyst for Quinnipiac.

That presents a challenge for moderate Democrats.

One of them, freshman Rep. Abigail Davis Spanberger of Virginia, announced Monday that she will back impeachment.

“The world, and our children, are watching as the foundation of the world’s longest-standing democracy is tested. Through this trying time, nothing is more important than fulfilling our obligation to defend the Constitution and protect our republic,” she said in a statement.

Rep. Elissa Slotkin, a Michigan Democrat representing a district that Mr. Trump won by 7 percentage points in 2016, wrote an op-ed to announce her support for impeachment.

“Over the past few months, I’ve been told more times that I can count that the vote I’ll be casting this week will mark the end of my short political career. That may be,” Ms. Slotkin wrote. “But in the national security world that I come from, we are trained to make hard calls on things, even if they are unpopular, if we believe the security of the country is at stake. … And this is one of those times.”

Mr. Van Drew came to the opposite conclusion. “Congressman for New Jersey’s 2nd District. Republican or Democrat — We are all American,” he said in a new biography posted on his Twitter account.

Speculation of his break with the Democrats began circling last week, though he denied it to reporters at the time.

He reportedly began to tell staffers over the weekend, and several of them quit by Sunday. They said they couldn’t support a party that aligns with Mr. Trump.

“We joined the office to serve the people of New Jersey’s 2nd Congressional District,” the staffers said in a letter. “We greatly respect Congressman Van Drew and are deeply saddened and disappointed by his decision. As such, we can no longer in good conscience continue our service in the congressman’s employ.”

Rep. Cheri Bustos of Illinois, chairwoman of the Democratic Congressional Campaign Committee, said the staffers are welcome to work for her operation “until they land new jobs that align with their values.”

Sen. Cory A. Booker and Gov. Phil Murphy, two senior New Jersey Democrats, said Mr. Van Drew’s move had less to do with principle and more to do with his political survival.

“He’s putting politics over the Constitution, he’s putting cuteness over courage, and he’s cutting and running,” Mr. Murphy said on CNN. “He apparently saw some poll numbers he didn’t like. He’s on the wrong side of impeachment.”

Rep. Steve Cohen, Tennessee Democrat, went further and called Mr. Van Drew a “traitor.”

Mr. Trump won Mr. Van Drew’s district by nearly 5 percentage points in 2016. With the president on the ballot again in 2020, the congressman may have calculated that his chances were better as a Republican.

But his voting record may have to undergo a transformation. He has voted for the president’s proposals about 7% of the time, according to analysis from FiveThirtyEight.

Mr. Van Drew was the only Democrat who publicly committed to opposing the articles of impeachment.

Rep. Collin C. Peterson, who joined Mr. Van Drew to vote against beginning the impeachment inquiry, told his local Minnesota radio station that Republicans were also courting him but he decided to stay with Democrats.

Mr. Peterson said he is still undecided on the impeachment vote, the local news reported.

One of the two articles of impeachment accuses Mr. Trump of abuse of power for inviting Ukraine to get involved in the 2020 election by investigating a political rival, former Vice President Joseph R. Biden. The other says the president has obstructed Congress by blocking witnesses and documents.

Only a majority vote is needed for articles of impeachment to pass the House. They would then head to the Senate, where it takes a two-thirds vote to convict and remove the president.

Senate Majority Leader Mitch McConnell, Kentucky Republican, said last week there is no chance that would happen.

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