(CNN) Senate Judiciary Committee Chairman Chuck Grassley, an Iowa Republican, suggested Monday that the President should hire a new lawyer if his current one is telling him that he can pardon himself.

"If I were President of the United States and I had a lawyer that told me I could pardon myself, I think I would hire a new lawyer," Grassley told CNN when asked if he agrees that President Donald Trump could pardon himself.

Trump tweeted Monday that he had the "absolute right to pardon myself" but would not do so because he'd done nothing wrong.

"As has been stated by numerous legal scholars, I have the absolute right to PARDON myself, but why would I do that when I have done nothing wrong? In the meantime, the never ending Witch Hunt, led by 13 very Angry and Conflicted Democrats (& others) continues into the mid-terms!" the President tweeted.

Trump's comments echo the stance that his lawyer, Rudy Giuliani, has taken. Giuliani said Sunday on ABC's "This Week" that Trump "probably does" have such power to pardon himself, but won't.

In addition, Giuliani told HuffPost in an interview that the President's power extends so far that "in no case can he be subpoenaed or indicted."

"I don't know how you can indict while he's in office. No matter what it is," Giuliani said. "If he shot James Comey, he'd be impeached the next day," Giuliani said to HuffPost. "Impeach him, and then you can do whatever you want to do to him."

Asked about Trump weighing whether he should pardon himself, Sen. Bob Corker said, "I don't know why any president would go down the path of talking in that manner."

"I'm very surprised that this President would talk about pardoning himself," Corker, a retiring Republican from Tennessee, told CNN. "I know he said he would never need to because he didn't do anything wrong, but why would you venture into that territory?"

A decision by Trump to pardon himself — or even his close allies like former campaign chairman Paul Manafort — could raise constitutional questions for Congress, as some Democrats have said that such pardons or the firing of special counsel Robert Mueller could be grounds for impeachment.

The second-ranking Republican in the Senate, John Cornyn of Texas, dismissed questions about Trump pardoning himself as "an academic argument."

"It sounds like a debate law students would have over what the technical power is," Cornyn told reporters on Capitol Hill on Monday. "I think it's a distraction because so far -- on a bipartisan basis -- the conclusion has been that there's no evidence of collusion and James Comey told him several times that he was not a target of investigation."

Maine GOP Sen. Susan Collins said Monday that if Trump pardoned himself it would have "catastrophic implications" for him, but she declined to say whether she viewed it as an impeachable offense.

"It may well be an open question debated by constitutional scholars, but there's no doubt that if the President were ever to pardon himself it would have catastrophic implications for him and our country," she said.

South Carolina Republican Sen. Lindsey Graham made similar remarks Monday.

"Politically, it would be a disaster," Graham said. "Legally, I don't know."

Texas Republican Sen. Ted Cruz said Monday he had not studied the issue so he would not weigh in, following an 18-second pause when he was first asked the question by reporters on Capitol Hill.

"That is not a constitutional issue I've studied, so I will withhold judgment," Cruz said after being asked a second time whether he agreed with the President that he could pardon himself.

When asked about Trump's comments Monday, GOP Sen. John Kennedy of Louisiana instead talked about the President's "management style."

"The President likes to tweet," Kennedy told reporters. "If he asked me my opinion, and he hasn't, I would suggest to him that tweeting less would not cause brain damage. But he likes to tweet, and he's the President and he's entitled to do that. That's his management style."

This story has been updated.