That is why, on a rainy night here, Crossroads, which was founded by the Republican strategist Karl Rove, gathered about 50 voters representing groups that it believes can be persuaded to vote against Mrs. Clinton — an all-white mix of young men, low-income adults, married mothers and politically moderate women.

One problem in developing negative messages about Mrs. Clinton, Republican strategists have found, is that she and her husband have survived so many controversies by dismissing them as partisan attacks. So the Republican organizations are seeking to develop lines of attack that resonate more deeply or raise unsettling questions about Mrs. Clinton’s character.

They showed the voters, who received $100, sandwiches and soft drinks for their time, more than a dozen 30-second ads. (Crossroads allowed a reporter to observe the focus groups under the condition that the participants’ names be withheld.)

The ads highlighted Mrs. Clinton’s deleting of emails from her private account, tried to tie her to President Obama, portrayed her as distant from middle-class Americans and sought to persuade women that they do not need to support her because of her gender.

But many, essentially, struck the same theme, depicting Mrs. Clinton as untrustworthy, an image that even Democrats supporting the Clinton campaign acknowledge is a weakness. About 57 percent of Americans do not believe Mrs. Clinton is honest and trustworthy, according to a CNN poll released June 2.

“She’s got an open wound, and part of our job is to pour salt in it,” said Glen Bolger, a co-founder of Public Opinion Strategies, the Republican polling firm that conducted the focus groups.

Image An ad shown to a focus group contests Mrs. Clinton’s comments that she and her husband were “dead broke” when they left the White House.

Mrs. Clinton’s allies point to relatively low trust numbers for Mr. Clinton in the 1992 and 1996 elections and his ability to win voters despite his personal failings.