(CNN) Under fire after a disastrous first debate and for mocking a former Miss Universe's physique, Donald Trump is turning to decades-old scandals for ammunition: Bill Clinton's extramarital affairs.

That strategy -- which enjoys little support within Trump's own party -- is the latest and one of the most striking demonstrations of the Republican presidential nominee's instinct for bomb-throwing and preference for risky personal attacks over political discipline and restraint. And some Republicans are warning that it could backfire.

Trump faces tremendous pressure to step up his game next month when he faces off against Hillary Clinton for their second general election match-up. But rather than lean on conventional tools such as mock debates or a media coach, he appears most eager to dredge up controversies from the Clintons' past that most Republicans are deeply wary of reviving.

In a talking points memo circulated to supporters this week obtained by CNN, the Trump campaign instructed surrogates to point to figures like Monica Lewinsky and Gennifer Flowers -- women that Bill Clinton has acknowledged having sexual relations with -- to counter the criticism the Republican nominee has received for attacking ex-Miss Universe Alicia Machado.

Mere moments after leaving the debate stage Monday night, Trump was already patting himself on the back for not going there in the first contest.

"I'm really happy I was able to hold back on the indiscretions in respect to Bill Clinton. Because I have a lot of respect for Chelsea Clinton," he told CNN's Dana Bash.

When asked what he would say, Trump added, "Maybe I'll tell you at the next debate. We'll see. But I'm very happy."

Clinton, for her part, is saying little when it comes to the topic of a spouse's past.

Gaggling with reporters on her plane Thursday, Clinton was asked whether she feels any obligation to object to a spouse's indiscretions being brought up in the campaign.

Clinton simply answered: "No."

Pressed again on Trump pointing to her husband's impeachment as evidence that the Clintons have a sordid past, Clinton responded: "He can say whatever he wants to say."

Republicans acknowledge that the former president's past indiscretions are a powder keg likely to blow up in Trump face.

On Capitol Hill, GOP lawmakers urged Trump this week to stay away from former President Clinton's affairs.

"We need to stay on the issues that are important to the American people, you know?" said Texas Rep. Bruce Babin, when asked whether Trump should bring up Lewinsky and others. "That's ancient history."

Others were even more direct in warning that personal attacks would only come back to haunt Trump.

Rep. Ryan Zinke, a Montana Republican, said Trump must stay focused on policy issues and steer clear of personal attacks, as he cited Clinton latching on to Trump's critique of Machado's weight.

"You see the personal attacks, she's right back to attacking Mr. Trump on previous things that were said or were alleged to be said. I think at the end of the day it's jobs, number one, national security, it's immigration, it's repealing and replacing Obamacare," Zinke said.

There is precedent for those warnings: Hillary Clinton's approval rating reached its peak after details about her husband's affair with Lewinsky began to surface.

Republicans who believe the issue is fair game argue that Clinton is vulnerable to questions about how she treated the women her husband had affairs with -- and less the fact that the affairs happened at all.

In 1992, Clinton sharply dismissed Flowers, who was then accusing her husband of adultery. As first lady, Clinton called her "some failed cabaret singer who doesn't even have much of a resume to fall back on."

Her husband later admitted that he did, in fact, have an affair with Flowers.

And in a letter to her friend that became public in 2014, Clinton also called Lewinsky a "narcissistic loony toon."

Clinton has had plenty of practice responding to Republicans on her spouse's past.

Earlier this year, for example, as Clinton began taking questions at a town hall in New Hampshire, GOP state representative Katherine Prudhomme O'Brien stood just feet from the candidate and began shouting about Bill Clinton.

After dismissing her once, Clinton forcefully responded.

"You are very rude, and I'm not ever going to call on you," Clinton said looking directly at the woman. "Thank you."

Prudhomme later said that she was asking about Juanita Broaddrick, Kathleen Willey and Paula Jones -- three women who have accused Bill Clinton of misconduct.

Clinton aides expect Trump, at some point, will at some point explicitly "go there" on Bill Clinton's past. But most remain skeptical that it will stick the way that the Republican nominee seems to hope.

"After his disastrous debate performance and his sexist attack on a former Miss Universe over her weight, Donald Trump is now trying to deflect by going after Hillary Clinton about her marriage," Brian Fallon, Clinton's spokesman, said Thursday. "As many Republicans have warned, this is a mistake that is going to backfire."