Senate GOP leaders don't back Cornyn call for Holder to resign

Senate Republican leaders on Tuesday said there should be an investigation of Attorney General Eric HolderEric H. HolderDem rep: Jim Crow's 'nieces and nephews' are in the White House Obama to attend Pittsburgh Steelers owner's funeral Ex-Uber employee who spurred sexual harassment probe to lead new publication MORE, but stopped short of joining Sen. John CornynJohn CornynDisconnect: Trump, GOP not on same page Juan Williams: Trump's 100 days wound GOP Trump wall faces skepticism on border MORE’s (R-Texas) call for his resignation.

Senate Republican Leader Mitch McConnellMitch McConnellDisconnect: Trump, GOP not on same page GOP senator: There will never be full U.S.-Mexico border wall Overnight Tech: Dem wants to see FCC chief's net neutrality plans | New agency panel on telecom diversity | Trump calls NASA astronaut MORE (Ky.) told reporters that many GOP lawmakers share Cornyn’s frustrations with the Justice Department.

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“We certainly need to have an investigation of what has happened, and I think John Cornyn speaks for a lot of us as to the frustration we feel about not only the national security leaks, the "Fast and Furious" matter — there's been a whole litany of problems coming out of the Justice Department,” McConnell said.

“I'm listening carefully to what my colleagues are saying. I think we're all unhappy with the performance of the attorney general,” he said.

Cornyn, a member of the Judiciary Committee and chairman of the National Republican Senatorial Committee, called for Holder to step down at a Judiciary Committee hearing Tuesday morning where the attorney general testified before lawmakers.

“You’ve violated the public trust in my view and by failing and refusing to perform the duties of your office,” Cornyn told Holder.

“Mr. Attorney General, it is more with sorrow than anger that I would say that you leave me no alternative but to join those who call upon you to resign your office.”

Holder is also under fire from the House, where Republicans have set up a panel vote next week to hold him in contempt if he does not provide documents related to the Fast and Furious gun-tracking operation.

Other GOP leaders in the Senate also stopped short of calling on Holder to resign.

Senate Republican Conference Chairman John ThuneJohn ThuneDisconnect: Trump, GOP not on same page Seven major players in Trump's trillion infrastructure push Trump’s great tech opportunity is in spectrum sharing MORE (S.D.) took a stance similar to McConnell’s.

“Clearly we need an investigation and we’re going to continue to press for that,” Thune said. “The question about whether or not he should resign is something that I’m listening carefully to what my colleagues are saying and I’ll probably make some determination about that,” he added.

Senate Republican Conference Vice Chairman Roy BluntRoy BluntDisconnect: Trump, GOP not on same page GOP senator: There will never be full U.S.-Mexico border wall This week: Congress returns to government shutdown fight MORE (Mo.) noted he is not a member of the Judiciary panel.

“The problem here is the direction of the country under this president and under this administration,” he said.

A spokesman for Senate Republican Whip Jon Kyl (Ariz.), another member of the Judiciary Committee, did not respond immediately to a request for comment.

Jordy Yager contributed to this story.