Not Sen. Jeff Flake.
Flake, the junior Arizona senator, told CNN that "some of Trump's positions" make it "very difficult for me" to support him.
"I hope that he backs off some of those," Flake said. "There's some sign that he will on on the religious test for people to enter here. I think he's finessing that. I'd like to see him go further."
"I don't know of anybody who really believes that. So that's not as serious. But when you say you're going to require a religious test for people to enter, or say that you're going to rewrite the libel laws to go after those who write bad things about you, that's fundamental and you know you've got to back off that kind of stuff."
McCain, the senior GOP senator, has a different take. He says GOP voters have had their say, so he will back Trump. And he worries that Hillary Clinton will continue Obama's foreign policy.
But McCain is sharply critical of Trump's immigration views -- and he knows full well the presumptive GOP nominee's remarks about Latinos could imperil his own reelection.
"It means that we have a challenge, obviously," McCain said when asked about Trump's unpopularity with voters. "First of all, it's a great challenge, because there are a lot of people who will just vote straight ticket. We know that from past history but also -- and that is going to make doing this even more difficult election, campaign for me. And I want to emphasize, I have taken every election with the utmost seriousness. I take this one with the utmost seriousness."
With his authorship of two comprehensive immigration bills, McCain said: "I have one thing going, and that is the Hispanic community does know me. I received the endorsement recently from the Hispanic Chamber of Commerce. So I believe that that can be very helpful, but it can't help if the majority of those who will be voting for the top of the ticket have been alienated or feel that that candidate would not be in their interest. And that's the top of the ticket."
McCain added that is the "reality" of the situation.
Yet the fact that McCain still supports Trump underscores the challenges he faces in courting his nominee's supporters while also wooing Hispanics. McCain said he wasn't sure if he'd campaign with Trump.
Asked if Trump hurts McCain, Flake added: "I don't think it helps anybody's candidacy. Although McCain is probably in a different class. McCain has enough independent stature to distance himself from some of these statements that Trump has made. Trump has actually gone after McCain on the POW kind of thing. And so I think John McCain will be just fine."