WASHINGTON — Even before the judicial oath was administered and Judge Brett Kavanaugh became Justice Kavanaugh, some on the political left were sounding calls to impeach. A month before the midterm election, that makes many mainstream Democrats nervous.

As both parties move on from the most bruising Supreme Court confirmation battle in a generation, Democrats hope to harness voter anger over the explosive proceedings and the narrow outcome, but not turn the midterm contest into a polarizing referendum on whether the party should try to remove Kavanaugh — an effort that would have little likelihood of succeeding.

Republicans and Democrats have put competing spins on how the confirmation fallout might play out at the polls. The GOP says the battle over Kavanaugh has energized its voters, who have lagged behind Democrats in previous measures of enthusiasm over the election.

“I think the Republicans are going to do great in the midterms,” President Trump told reporters on Air Force One en route to a rally in Topeka, Kan., Saturday evening. “I think we have a momentum that hasn’t been seen in years.”

Democrats say the debate over Kavanaugh has amped up the anger that many women already felt toward Trump and the Republicans, and will lead to higher turnout on their side.

Both could be right, at least in part. The Kavanaugh fight could produce opposite results in the contests to control the Senate and the House.

Greater Republican enthusiasm to vote could help GOP candidates in this year’s highly contested Senate races. Most of those are taking place in conservative states that have Democratic senators, such as Indiana, Missouri, Montana and North Dakota.

At the same time, increased turnout among women could help Democrats trying to flip Republican-held House seats in suburban areas, including five longstanding Republican districts in Southern California that Democrats hope to win this year.

Democrats need to pick up 23 additional seats nationwide to take control of the House. Polls in many of most contested districts indicate that goal is reachable but by no means assured.

A new round of Senate polls in four states released Sunday by CBS and YouGov indicated that most voters who said the Kavanaugh fight had increased their motivation to vote were partisans who already were highly likely to vote for their party’s choice.

But in the closest race of the four, in Arizona, the polling indicated that the Kavanaugh issue might help the Democratic candidate, Rep. Kyrsten Sinema, who held a slight lead, 47% to 44%, over Republican Rep. Martha McSally.

Among the small group of likely voters who said they might still change their minds about which candidate to back, 3 in 10 said Kavanaugh’s confirmation would make them more likely to consider voting for a Democrat, compared to 1 in 10 who said the confirmation would make them more likely to back a Republican, the poll found.

As both parties analyzed polling data, Trump and his senior aides dashed any expectation that they might strike a unifying stance in the wake of a battle that pitted Americans against one another as much as any political clash in recent memory.

“Congratulations to Justice Kavanaugh and President Trump!” senior White House aide Kellyanne Conway said Sunday, echoing the triumphal tone struck by the president and his supporters in the Senate in the wake of Kavanaugh’s 50-48 confirmation on Saturday.

Interviewed on ABC’s “This Week,” Conway expressed no qualms about the heated tenor of the confirmation process, including the president’s public taunting at a campaign-style rally of Christine Blasey Ford, the Northern California research psychologist who testified that Kavanaugh sexually assaulted her when they were high school students.

“All of us were very respectful to Dr. Ford,” Conway said. She said Ford’s allegations in no way “tainted” Kavanaugh’s tenure, which could last decades.

Dismayed as they were by the outcome, even some Democrats who led the charge against Kavanaugh shied away publicly from any talk of impeachment.

“I’m much more focused on the here and now,” said Sen. Mazie Hirono (D-Hawaii), also interviewed Sunday on ABC. “Focus like a laser beam on the elections.”

Sen. Chris Coons (D-Del.) called impeachment talk “premature.” Coons was a key Judiciary Committee figure in the confirmation hearings, helping persuade his Republican friend Sen. Jeff Flake of Arizona to demand a reopening of Kavanaugh’s FBI background check.

Discussing impeachment prospects “at this point isn’t necessarily healing us and moving us forward,” said Coons, interviewed on NBC’s “Meet the Press.”

Even though Democrats do not want to appear overly confident about winning control of the House, some have already raised the issue of investigating Kavanaugh for untruthfulness if they gain the majority and key committee chairmanships come into their hands.

Rep. Jerrold Nadler of New York, the ranking Democrat on the House Judiciary Committee, who would probably take over the chairmanship from Rep. Robert W. Goodlatte (R-Va.) if Democrats win control of the House, explicitly raised the issue even before Kavanaugh’s confirmation.

“If he is on the Supreme Court, and the Senate hasn’t investigated [Kavanaugh], then the House will have to,” Nadler told ABC a week ago. “We would have to investigate any credible allegations of perjury and other things that haven’t been properly looked into before.”

Democratic Rep. Ted Lieu of Torrance has gone further, joining with fellow Judiciary Committee member Rep. Luis V. Gutierrez (D-Ill.) in calling for a start to impeachment proceedings against Kavanaugh if an investigation shows he lied in his testimony.

In practical terms, impeachment of a justice is an extreme rarity.

Impeachment requires a majority vote in the House to present charges that would be heard by the Senate. Two-thirds of the Senate would be needed to convict — an extremely high threshold to overcome.

Proceedings against a sitting justice have been brought only once – against Samuel Chase in 1805. He was impeached by the House but acquitted in the Senate.

The Democratic leadership has already spent months working to dampen public talk about trying to impeach the president for fear of energizing Trump’s base and scaring off swing voters.

House Minority Leader Nancy Pelosi of San Francisco could not contain a flash of exasperation about getting bogged down in similar debate over Kavanaugh at this juncture.

Trying to impeach the new justice “would not be my plan,” Pelosi said during an appearance Tuesday at the Atlantic Festival in Washington. “I have enough people on my back wanting us to impeach the president.”

Republican Gov. John Kasich of Ohio, interviewed on CNN, said he believed the GOP would have done better to avoid turning the Supreme Court nomination into an overtly partisan battle.

“The court, it could be a short-term win” for Republicans, Kasich said.

“Let me tell you what I think a president should do. You’re going to nominate a Supreme Court justice, and you’re a Republican, you know you’re going to have a conservative,” he said. “But it would make sense to work with a Democrat who would say, ‘OK, I know it’s going to be conservative; all right, let me help you to pick somebody so that we don’t go through this.’ ”

laura.king@latimes.com

Twitter: @laurakingLAT

Times staff writer David Lauter contributed to this report.