But he's one of the few willing to air those worries in public.
Most GOP senators were silent yesterday, a day after Corker charged that the White House was an "adult day care" and Trump could set the nation "on the path to World War III."
The only senator who publicly hinted at similar concerns was Iowa Sen. Chuck Grassley, who said both Trump and Corker should "cool it."
"And I think it would help if the president would be the first to cool it," he added.
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But Trump's enduring popularity with a segment of the GOP base serves as a political muzzle that keeps most elected Republicans from saying anything similar, even those who believe it to be true.
The president slammed the interview today on Twitter. Said Trump: "The Failing @nytimes set Liddle' Bob Corker up by recording his conversation. Was made to sound a fool, and that's what I am dealing with!"
"I don't see how it's productive, and I think that two words would kind of answer your question from my point of view: Cool it," he said. "I think it would be better if we stuck to the issues and leave personalities out of it."
A few other Republican senators who provided public views yesterday avoided aligning themselves with Corker.
"You'll have to ask Sen. Corker what led him to make that statement. I haven't made that statement," Sen. Marco Rubio of Florida said of Corker's suggestion that Trump could take the country into another world war.
"Any of us who've worked with Sen. Corker know that he speaks his mind," Flake said, demurring on whether he shares Corker's view that the White House has become an "adult day care center."
"I agree with him on some things, I've supported a lot of his agenda, some things I've disagreed with and continue to do so," Flake said of Trump.
The Associated Press sought to contact all 52 Republican senators yesterday for their response to Corker's comments and ask whether they believe Trump is fit for office, a question Corker declined to answer in the Times interview.