Senate Republicans don’t think it would be a good idea for President Trump to fire Special Counsel Robert Mueller. But few were willing on Monday to elaborate on what steps need to be taken to protect the special counsel, even after the President and his personal lawyer lashed out at Mueller by name over the weekend.

“I have zero concern that the President is going to fire Mueller. Zero,” Sen. Lindsey Graham (R-SC) told reporters on Capitol Hill Monday, despite having introduced legislation that would prevent Trump from doing so.

Graham — who on Sunday said that firing Mueller would be “the beginning of the end” of Trump’s presidency – told reporters on Monday that he introduced the bill protecting the special counsel “to let people know where I stand.”

There are currently two bills that would address the threat of Trump terminating Mueller, each with Republican cosponsors.

Robert Mueller should be able to continue his investigation unimpeded, which is one of the reasons I introduced the Special Counsel Integrity Act with @ChrisCoons. — Senator Thom Tillis (@SenThomTillis) March 19, 2018

The Senate Judiciary Committee held a hearing on them months ago, and Judiciary Chairman Chuck Grassley (R-IA) said on Monday that the committee was still working on working out the differences in the pieces of legislation. Even still, he sounded skeptical that Trump would ax the special counsel.

“I don’t think the President would do that. He shouldn’t do it,” Grassley said, adding that he had “great faith in” Mueller

“The best thing for him as President — since after almost one year, there’s been no show of collusion — seems to me like he’s coming out looking pretty good at this point and he ought to just let it play out, ” he said.

Sen. John Thune (R-SC), the No. 3 Senate Republican, said he didn’t think the legislation was “necessary.”

“I just think that they would be well served not to do anything that messes with or disrupts this process,” he said.

Likewise, Sen. John Cornyn (R-TX), the Senate GOP whip who also sits on the Judiciary Committee, raised concerns about “picking that fight” with the President.

John Cornyn says he doesn’t think legislation shielding Bob Mueller is needed. Trump will never fire Mueller, he says. “I don’t think that’s going to happen, so I just think it’s not necessary. Adds “I don’t see the necessity of picking that fight right now.” — Laura Litvan (@LauraLitvan) March 19, 2018

Trump— perhaps provoked by the fallout over Attorney General Jeff Sessions’ firing of a former top FBI official, or by recent reports that his business had been subpoenaed, or by ongoing negotiations over sitting for an interview with the special counsel — tweeted Saturday that the Mueller investigation “should never have been started. On Sunday Trump alleged that Mueller’s team was filled with “hardened Democrats.” His personal lawyer John Dowd called for Mueller’s firing on Saturday — in a statement he first said was being made on behalf of the President, but then walked back by clarifying that it was from Dowd personally.

The White House lawyer representing Trump in the investigation, Ty Cobb, put out a statement Sunday evening claiming that “the President is not considering or discussing the firing of the Special Counsel, Robert Mueller.”

Cobb’s statement was enough to assure many Republicans, such as Sen. Cory Gardner (R-CO), another member of the GOP leadership team.

“The White House has said that they’re not going to do anything on this, so that’s important,” Gardner said.

The one exception was Sen. Jeff Flake (R-AZ), a frequent Trump critic who is not running for re-election this year.

“Just a week ago, he said he wasn’t going to be firing Tillerson, too,” Flake said, referring to Rex Tillerson, the secretary of state whom Trump fired by tweet on Tuesday. “So preemptively, it would behoove our leadership to be forceful and say, ‘This is the line and you cannot cross.'”

Nonetheless, Flake said he had constitutional concerns about legislation protecting Mueller, a potential issue that Grassley also raised.

In January, Senate Majority Leader Mitch McConnell (R-KY) said that there was no need for legislation to protect Mueller, because “there’s no effort underway to undermine or to remove the special counsel.” His spokesman did not respond to TPM’s inquiry as to whether McConnell had privately warned Trump against removing Mueller.

Sen. Orrin Hatch (R-UT), the Senate President pro tempore, in a statement Monday, suggested he had directed such warnings at the White House.

“My conversations with the White House have led me to believe legislation is not necessary at this point because I do not believe the President would take such a foolish action,” Hatch said.