Kentucky Senate hopeful Rand Paul found few allies in the Senate GOP Conference on Thursday after expressing opposition to part of the 1964 Civil Rights Act.

Paul, a tea party favorite who won the GOP nomination for Senate on Tuesday, has come under fire for saying he disagrees with the landmark civil rights law’s prohibition on segregation policies at privately owned facilities open to the public. Paul has since said he does not support repealing the Civil Rights Act.

But that didn’t stop the controversy from exploding on Capitol Hill, where many Republicans tried to distance themselves from his comments. “There is no doubt in my mind that the interstate commerce clause has been properly used by the courts and the Congress,” Sen. Lindsey Graham (R-S.C.) said.

Judiciary ranking member Jeff Sessions called Paul’s comments “wrong.”

“I think that was settled a long time ago and the country is better off,” the Alabama Republican said of the law.

“Things that welcome the public should welcome everybody,” he added. “I think he’s wrong.”

Sen. John Thune said that Paul’s comments are not universally accepted by Republicans and that Paul will “have to answer for” his position. “There are positions that some of our candidates will take that a lot of us won’t agree with,” the South Dakota Republican said.

In a statement, Don Stewart, spokesman for Minority Leader Mitch McConnell (R-Ky.), noted that his boss worked in the Senate as an intern in 1964 for Sen. John Sherman Cooper (Ky.), one of the key GOP supporters of the Civil Rights Act.

“Among Sen. McConnell’s most vivid memories and most formative events in his career was watching his boss Sen. John Sherman Cooper help pull together the votes to break the filibuster and pass the Civil Rights Act of 1964. He has always considered the law a monumental achievement for the country and is glad to hear Dr. Paul supports it as well,” Stewart said.

Other Republicans, however, sought to avoid any direct criticism of Paul while highlighting their support for the Civil Rights Act.

When asked during a press conference whether they agreed with Paul’s assertions, Thune, Republican Conference Chairman Lamar Alexander (Tenn.) and GOP Sens. Judd Gregg (N.H.) and George LeMieux (Fla.) shifted uncomfortably on stage. Alexander then stepped forward to answer the question, stressing his support for the Civil Rights Act.

“No. 1, I support the Civil Rights Act, and No. 2, the people of Kentucky will elect the next Senator,” Alexander said.

Other Republicans, meanwhile, tried to avoid the issue altogether. “I don’t want to comment on something that I haven’t heard,” Sen. Saxby Chambliss (R-Ga.) said.

And National Republican Senatorial Committee Chairman John Cornyn (Texas) defended Paul and accused Democrats of twisting Paul’s words.

“Rand Paul has unequivocally stated that he does not support any efforts to repeal the Civil Rights Act of 1964 and that he is deeply opposed to any and all forms of racism and segregation. Unfortunately, this appears to be another partisan attack fabricated by the Democrats in order to distract from the issues that Kentuckians care about, like Jack Conway’s support for the Democrats’ massive health care law,” Cornyn said.