“I don’t know what he means by that,” Texas Sen. John Cornyn, the chairman of the National Republican Senatorial Committee, told POLITICO on Thursday. “I support nondiscrimination of people, so I would need to talk to him to see what precisely his concerns were.”

Kyl — the No. 2 Republican in the Senate — said he watched Paul’s exchange with Maddow on Wednesday night and suggested that Paul should have avoided “engaging in a theoretical debate with her.”

“I think the two of them were having a bit of good time having a debate like you had at 2 a.m. in the morning when you’re going to college, but it doesn’t have a lot to do with anything,” Kyl said.

Asked if he agreed with Paul’s view, Kyl said: “You’re trying to go back to the 1960s and redebate all that, and I’m just not going to go to it. I think he was trying to say that.”

Alabama Sen. Jeff Sessions, the ranking Republican on the Judiciary Committee, said Thursday that he can understand how Paul reached that conclusion – based on his libertarian-leaning views – but he said that the law is settled, should not be changed and the country should not reopen the “painful” period in American history.

“My view is that issue has been settled – the courts have ruled on it,” Sessions said. “If you open a restaurant, a hotel to the public then you can’t discriminate on who you allow to come in and out, I think that’s settled. I think America is better off that the segregation views are over, and that played a role in it. ... But if you take a more libertarian view, a stronger view of private party, you could reach the conclusion he reached.”

Asked if he agreed with Paul’s conclusion, Sessions said: “I don’t support that.”

On Thursday, Paul went into overdrive to contain the fallout of his damaging statements from the night before.

Speaking with Ingraham, Paul chalked up the focus on his comments to unfounded attacks by the “loony left.”

"I’ve never really favored any change in the Civil Rights Act," he said.

He reiterated that view in his statement – although he did not say explicitly that he thought the federal government should have stepped in to prevent discrimination by private businesses as opposed to government agencies.

“The issue of civil rights is one with a tortured history in this country. We have made great strides, but there is still work to be done to ensure the great promise of Liberty is granted to all Americans,” Paul said.

“This much is clear: The federal government has far overreached in its power grabs. Just look at the recent national healthcare schemes, which my opponent supports. The federal government, for the first time ever, is mandating that individuals purchase a product. The federal government is out of control, and those who love liberty and value individual and state's rights must stand up to it.”

He dismissed the flap over his comments as proof that “the liberal establishment is desperate to keep leaders like me out of office,” and he said that there are sure to be more “more wild, dishonest smears during this campaign.”