He discussed it himself in passing at his one public event on Thursday, a rally in Bedford, N.H.

“The American people have had it with years and decades of Clinton corruption and scandal, corruption and scandal. And impeachment for lying. Impeachment for lying. Remember that? Impeach,” Mr. Trump said.

Democrats believe such critiques will become only harsher and more pointed.

Mrs. Clinton declined to wade into the topic on Thursday. “I’m not going to comment on how he runs his campaign. You’ll be able to see — we have two more debates — what he says and what I say,” told reporters.

But Republicans have questioned whether such a line of attack would be effective. Several prominent party members, including Gov. Asa Hutchinson of Arkansas, who as a congressman helped lead the impeachment case against Mr. Clinton 20 years ago, have said publicly that they believe Mr. Clinton’s behavior is a dead issue and that Mr. Trump should “look to the future.”

Correct the Record, a “super PAC” that defends Mrs. Clinton, has troves of background on women, including Juanita Broaddrick and Kathleen Willey, who have accused Mr. Clinton of sexual assault. The group has also prepared a vicious counterattack on Mr. Trump’s marital history, which includes two divorces and infidelity.

Some of Mr. Trump’s advisers have tried to suggest a narrower line of attack: focusing on allegations that Mrs. Clinton tried to discredit women who said they had been harassed by Mr. Clinton. Chief among those suggesting this approach is Roger Stone, the longest-serving Trump adviser, who wrote a book called “The Clintons’ War on Women,” which lays out allegations from Ms. Broaddrick and Ms. Willey, which the Clintons or their lawyer David Kendall have denied. “The issue of Bill Clinton and women is not about marital infidelity, adultery or ‘indiscretions,’” Mr. Stone said.