Several Republican senators warned Tuesday that the verdict against Donald Trump in the E. Jean Carroll case could pose significant challenges for the former president in his 2024 bid.

«The fact is, I don’t think I can win the presidency,» Senator John Cornyn of Texas told reporters on Capitol Hill. «Regardless of what you think of him as an individual, for me, eligibility is… the only criteria.»

When asked if he could support someone who has been found guilty of sexual assault as a candidate for president, Senator Mike Rounds of South Dakota told reporters: «It would be hard for me to do that.»

«You’ve never liked hearing that a former president has been found, in civil court, guilty of those kinds of actions,» Rounds said. «A lot of us focus on what we’ve been saying for some time, that we’re looking for one person to lead this party together, and we hope those people will come forward.»

Sen. Bill Cassidy of Louisiana said the verdict is clearly troubling.

He has been declared civilly responsible. How could it do more than create concern? Cassidy said.

Senator John Thune of South Dakota suggested the verdict was most likely part of «a continuous drumbeat» throughout Trump’s candidacy.

He said that while many voters appear to have taken the view that prosecutors are «going after» Trump, «people will have to decide if … they want to deal with all the drama that will surround him.»

Senator Mitt Romney of Utah, a frequent critic of Trump, said a jury of «Trump’s peers found him guilty of sexual assault and awarded $5 million to the person who was harmed.»

“I hope that the jury of the American people has come to the same conclusion about Donald Trump,” he said.

A New York jury found Trump responsible for sexually abusing Carroll in a Manhattan department store nearly three decades ago. The jury awarded Carroll $5 million in damages for his assault and defamation claims, but said Trump was not responsible for Carroll’s alleged rape.

Trump, who has always denied Carroll’s claims, responded to the verdict on his social media websitecalling the verdict “A DISGRACE” and suggesting that he had been subjected to a “VERY UNFAIR PLAY”.

Some Senate Republicans dodged questions about the case.

Senator Marsha Blackburn of Tennessee told an NBC News reporter: «I don’t do walks and talks.»

Senator Lindsey Graham of South Carolina, one of Trump’s main allies, focused his criticism on «the New York legal system» and said it was «off the rails when it comes to Donald Trump.»

In his remarks on Capitol Hill, Cornyn suggested that «the public is tolerant of more misconduct by public officials these days than in the past» and that he was «significantly» tolerant of Trump, who was indicted by a grand jury last month for Manhattan in a case of silent money.

But, Cornyn said, Trump appears to be narrowly focused on his core supporters without appealing to a «broader spectrum of people.»

“He has a solid base of support, but you can’t win a general election with your base alone,” Cornyn said. «So, to me, that’s the reason why I don’t think he can be cast.»

Meanwhile, Sen. Cynthia Lummis of Wyoming argued that the verdict will not «make a difference to Trump supporters or Trump opponents.»