ST. LOUIS — Hillary Clinton ended up helping Donald Trump repair some of the damage from his lewd comments about women this weekend when she ran hard left on the Supreme Court — reinforcing the one overriding reason conservative Republicans have for voting for their flawed presidential nominee.

Her promise to use Supreme Court nominations to push a left-wing agenda did more than anything Mr. Trump said during the debate to win back his supporters, conservative leaders said Wednesday. That included evangelical voters who were repulsed by a 2005 videotape that surfaced over the weekend showing the Republican nominee using vulgar language to boast of his sexual exploits.

“I believe it justifies overriding other concerns like those generated by this tape,” said the Rev. Frank Pavone, national director of Priests for Life.

“Virtue exercised in our own personal choices is important, but policies contain or contradict virtues as well, and there is a corruption in our public policy right now,” he said. “So it is not only that it outweighs the personal failing, of which of course he is repudiated himself and is repenting of, but corruption and immoral outrageous are also incarnated in public policies.”

Mrs. Clinton, the Democratic presidential nominee, never mentioned the Constitution in her answer to a question about the justices she would nominate. Instead, she vowed to pick judges who would pursue abortion rights and impose new carve-outs of First Amendment protections for political speech.

“I have very clear views about what I want to see to kind of change the balance on the Supreme Court,” Mrs. Clinton said during the debate.

Mr. Trump pledged that as president he would nominate “people that will respect the Constitution of the United States,” including the Second Amendment.

“While that exchange didn’t make headlines, it may have been the most important exchange of the evening,” said Gary Bauer, president of the advocacy group American Values.

He said Mrs. Clinton’s pledge is a wake-up call for all Republican voters.

“Every part of the Republican coalition — economic conservatives, national defense conservatives and social conservatives — have reason to fear a Supreme Court with one to three more appointments like the ones that Barack Obama has already put on the court,” he said. “Voters that don’t understand that are running the risk of losing everything that they hold dear because of a 10-year-old tape with inappropriate language on it.”

He said values voters are particularly important to Mr. Trump.

“It is a narrowly divided country, and it doesn’t take much. It only takes peeling away 1 percent of values voters or causing a couple percent to stay home,” said Mr. Bauer. “So it is obviously a worrisome situation.”

The death of Justice Antonin Scalia in February added urgency to the Supreme Court issue. Senate Republicans’ refusal to act on President Obama’s nomination of Merrick Garland, a federal appellate judge, guarantees that the next president will make at least one appointment to the high court.

The advanced ages of several justices have invited speculation that the next president could make two more nominations to the Supreme Court.

Conservatives are determined to balance Mr. Obama’s two recent Supreme Court appointments — Justices Sonia Sotomayor and Elena Kagan — to protect against efforts to weaken Second Amendment gun rights and Fifth Amendment property rights, which some view as under siege from federal regulators such as those at the Environmental Protection Agency.

Overriding the high court’s decisions that made same-sex marriage and abortion the law of the land are also on conservatives’ wish list for the court.

The vacancy on the nine-member bench has highlighted the court’s close ideological divide. The justices deadlocked 4-4 in June on a challenge to Mr. Obama’s executive amnesty for some illegal immigrants, leaving in place a lower-court ruling that blocked implementation of the president’s plan.

Mr. Trump delivered a strong debate performance Tuesday at Washington University, but doubts persists about whether it was enough to repair damage wrought by the videotape — much less expand his support to overtake Mrs. Clinton in battleground states.

Democratic strategist Jim Manley said Mrs. Clinton answered the Supreme Court question honestly and had no reason to fear that she unwittingly energized conservative voters.

“These guys are just looking to use any justification they can at this point in time to continue to support Trump,” he said.

Adam Bozzi, a spokesman for End Citizens United, said Mrs. Clinton’s agenda for the Supreme Court has broader appeal than to only far-left voters, especially on his group’s issue.

Voters across the political spectrum applauded Mrs. Clinton’s promise to overturn the Supreme Court ruling in 2010 that allowed unlimited political spending by corporations, associations and unions, said Mr. Bozzi.

Overturn the Citizens United ruling was a centerpiece of Mrs. Clinton’s debate answer.

“Hillary Clinton’s call to reverse Citizens United will energize voters across the country who want to restore a voice for hardworking families in our elections,” said Mr. Bozzi.

The videotape, which caught Mr. Trump on a hot mic talking to “Access Hollywood” host Billy Bush aboard a bus en route to a cameo appearance on a soap opera, was the last straw for many Republicans who were uncomfortable with their party’s nominee.

Mr. Trump boasted that he could kiss beautiful women and grab their private parts because he was a celebrity. He also regaled Mr. Bush with a story about his failed attempt to seduce a married women.

Dozens of Republican Party leaders came out in opposition or withdrew their endorsements of Mr. Trump. Some called on him to quit the race, which Mr. Trump firmly refused.

Carrie Severino, chief counsel for the conservative Judicial Crisis Network, said the Supreme Court question alone has the potential to expand Mr. Trump’s base.

“Vast majorities of the country do not want the court to shift left, and its undeniable that would happen if Hillary Clinton is elected,” said Ms. Severino, a former clerk for Supreme Court Justice Clarence Thomas.

“For a lot of people, the Supreme Court is the No. 1 reason that they want to vote for Donald Trump. Really, it is a vote against Hillary Clinton having any say about who is on the Supreme Court,” she said.

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