President Trump’s campaign team and advisers said Tuesday that Democrats’ effort to impeach him will backfire in 2020 in the face of public sentiment against impeachment and Mr. Trump’s strong economic record.

A day after Democrats on the House Judiciary Committee subpoenaed former White House counsel Don McGahn to testify whether the president obstructed justice, Trump campaign national press secretary Kayleigh McEnany said Democrats “have never stopped trying to overturn the lawful results of the 2016 election.”

“Now that the Russia hoax has failed, they are turning to impeachment, which is equally ridiculous,” Ms. McEnany said. The “2020 Democrats are increasingly playing to the radical fringe of their party and are even willing to destabilize and divide the country to do it.”

White House Deputy Press Secretary Hogan Gidley said Democrats are pushing impeachment because their failure to do so would make the last two years of investigating the president look like a “waste.”

“It’s pretty clear what [Judiciary Committee Chairman] Jerry Nadler and the Democrats are up to,” Mr. Gidley told reporters. “They don’t want to get to the truth at this point, I don’t know what Jerry Nadler thinks he’s going to get that [special counsel] Robert Mueller didn’t.”

Mr. Trump said Tuesday night that he is opposed to current and former White House aides testifying to Congress after they already had cooperated with the Mueller probe.

“There is no reason to go any further, and especially in Congress where it’s very partisan — obviously very partisan,” the president told The Washington Post in an interview.

House Speaker Nancy Pelosi tried to tamp down her party’s agitation for impeachment during a conference call Monday night. She also told Democrats in a letter that “the facts regarding holding the president accountable can be gained outside of impeachment hearings.”

With Mr. Mueller’s report finding no coordination between the Trump campaign and Russia, a minority of voters — 34% — support starting an impeachment effort, according to a Morning Consult/Politico poll released Tuesday.

But the survey also showed how partisan divisions over impeachment are putting Democrats in a box and galvanizing the president’s supporters. Among Democratic voters, 59% favor impeachment, while 82% of 2016 Trump voters say impeachment should not be done.

Already several Democratic presidential candidates, such as Sen. Kamala D. Harris of California, Sen. Elizabeth Warren and Massachusetts and Rep. Eric Swalwell of California, have advocated for impeachment.

“They’re so desperate to stand out among the field of socialist Democrats, they’ll say anything for a little attention,” Ms. McEnany said.

The poll showed Mr. Trump’s job-approval rating has dropped to 39%, the lowest point of his term in that survey. The Mueller report cited numerous instances in which the president tried to compel aides to stop the Russia investigation, but said they failed to follow Mr. Trump’s directions.

Republican J.W. Verret, a former Trump transition official who is an associate law professor at George Mason University, said the president “dangled pardons in front of witnesses to encourage them to lie to the special counsel, and directly ordered people to lie to throw the special counsel off the scent.”

“This elaborate pattern of obstruction may have successfully impeded the Mueller investigation from uncovering a conspiracy to commit more serious crimes,” Mr. Verret wrote in The Atlantic. “At a minimum, there’s enough here to get the impeachment process started.”

While Democratic voters want Mr. Trump impeached, some Democratic lawmakers are pointing to Republicans’ impeachment of President Bill Clinton in 1998, which led to a backlash against the GOP in the midterm elections that year. Rep. Stephen Lynch, Massachusetts Democrat, told CNN that impeachment “may play into President Trump’s hands” in 2020.

“I think, politically, for the Democrats, we face that same danger here,” Mr. Lynch said.

Sen. Lindsey Graham, South Carolina Republican and a White House ally, said the rising calls for impeachment show that Mrs. Pelosi “is not in charge of the Democratic Party.”

“They’re going to be stampeded to impeach Trump because they hate him so much, and I hate it for the country, I hate it for the president, but it’s going to result in him getting reelected,” Mr. Graham said on Fox News. “The Mueller report to me is vindication of President Trump. [But] the Democratic Party doesn’t accept the fact that President Trump won. So, at the end of the day, we’re just going to have to deal with this in 2020 at the ballot box.”

Trump campaign officials and advisers say a push for impeachment will turn off most voters, given the results of the Mueller probe and the president’s record on national security and the economy.

“The president has a very strong record to run on,” White House senior adviser Jared Kushner said Tuesday at a forum hosted by Time magazine.

“The difference this time is that we have a lot of professionals, a lot more resources to be able to do it, so we’re going to build a great campaign. But most importantly, it’s going to be [about] where the country’s going.”

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