(CNN) President Donald Trump's latest tirade against Robert Mueller's investigation does not appear to have prompted many Capitol Hill Republicans to reconsider the need for legislation to protect the special counsel.

Instead, GOP lawmakers maintained Tuesday that additional protections aren't necessary all but offered a sobering warning: any move by Trump to oust Mueller would be cataclysmic for his presidency.

Senate Majority Leader Mitch McConnell told CNN, "I think he'll be allowed to finish his job."

"I haven't seen clear indication yet that we needed to pass something to keep him from being removed because I don't think that's going to happen," the Kentucky Republican added.

While Senate Democrats huddled with party leaders on Tuesday to discuss potential responses to Trump, Senate Republicans avoided the topic altogether during their weekly party lunch.

"It didn't even come up," said Sen. John Kennedy of Louisiana.

Following Monday's FBI raid related to his personal lawyer, Michael Cohen, Trump showed signs of increasing anger and his response has been to unleash -- once again -- on the Russian investigation. On Monday afternoon, Trump refused to say he wouldn't fire Mueller and Tuesday morning he tweeted that the investigation was a "witch hunt" and that "Attorney-client privilege is dead!"

"It's a disgrace, it's, frankly, a real disgrace, it's an attack on our country in a true sense. It's an attack on all we stand for," Trump told reporters at the White House Monday afternoon just as news broke of the FBI raid.

"Why don't I just fire Mueller? Well, I think it's a disgrace what's going on. We'll see what happens," Trump added. "And many people have said, you should fire him."

But members in his own party -- just as they did weeks ago -- are reluctant to intervene, saying Trump's comments don't change the fact that they don't see a need to take further action to protect Mueller.

"I believe that Director Mueller has an important job to do, and I believe he can discharge that job in a professional and impartial sort of way. So my advice to anybody would let Director Mueller do his job," said the Senate's No. 2 Republican, John Cornyn of Texas.

Pressed what he'd do if Trump acted to fire Mueller, Cornyn said, "I'm not going to speculate as to what we would do because I think there would be serious repercussions."

"It's hard to predict what that would look like. So, I think Director Mueller ought to be free to do his job and let the courts and let the lawyers work it out," Cornyn said.

Other Republicans downplayed Trump's most recent comments, arguing they didn't reveal anything new about the President's posturing against the Russia investigation.

"I think thematically he's said similar things before so I don't think that that's anything new in my opinion," Sen. Thom Tillis, a Republican from North Carolina, said.

Over and over again, Republicans insisted Trump wasn't about to fire Mueller.

"I don't think he would do that," Iowa Sen. Joni Ernst said. "There's always a possibility. He has that prerogative, but so far he's declined to do so and I think it's in his best interest if he does not."

But sources familiar tell CNN that the latest raid on Trump's personal lawyer and longtime confidant has shaken the President in new ways. Cohen had become a surrogate family member to the President, and has been spotted semi-regularly at the White House, at times meeting with Trump or dining with the first lady.

Democratic Sen. Richard Blumenthal of Connecticut predicted that the news could lead to the President being even more "impulsive and wrathful."

Last year, there were two bipartisan bills introduced in the Senate that would protect the special counsel from being fired. The Senate Judiciary Committee held a hearing on the measures in the fall, but there's been little action on the legislation since.

Senate Foreign Relations Chairman Bob Corker, a Tennessee Republican, said he would back such legislation but that it's not yet necessary.

"I would sign onto legislation that protected him, but I just don't see a lot of momentum around it," Corker said. "I think we'd be better off with (the President) knowing that it'd be a huge problem if he did something then unsuccessfully passing legislation."

Across the aisle, a Senate Democratic source told CNN that Democrats in the chamber just huddled with party leaders to talk about "what if" Trump fires Deputy Attorney General Rod Rosenstein or Attorney General Jeff Sessions. They discussed immediately calling for document preservation and for Republicans who have been warning about this to join with them if it happens.

Sen. Chris Coons, the Delaware Democrat who co-sponsored one of the special counsel protection bills with Tillis, said legislation is "more urgent than ever" in light of Trump's comments Monday.

"I appreciate that all of my Republican colleagues appreciate the risk to the rule of law that an inappropriate, abrupt firing of the special counsel by the President would create," Coons said. "I am deeply puzzled by the lack of urgency or motivation to take some simple measured steps to address it."

Coons said he planned to speak with Tillis and Grassley soon for an update on the measure.

Tillis said the special counsel protection bills have merit, and he would still like to see them reconciled. But he noted that there were scores of predictions that Mueller's firing was imminent back in August 2017, when the bills were first introduced.

Sen. Lindsey Graham, a South Carolina Republican who co-sponsored the other special counsel bill with New Jersey Democrat Sen. Cory Booker, says he'd be happy to move a bill if Grassley wants to do so. But he doesn't see an imminent need because he doesn't believe Trump will fire Mueller.

"I've talked to Trump. I think he understands the consequences," Graham said. "I think it'd be the end of his presidency, for the political chaos."

This story has been updated with additional comments from lawmakers.