Sen. Ted Cruz moved Tuesday to put some distance between himself and fellow presidential hopeful Donald Trump, pushing back against the billionaire businessman’s call to halt Muslim visitors to the U.S. as part of a controversial anti-terror plan.

GOP insiders, though, were waiting to see whether Mr. Cruz or anyone other Republicans would be able to capitalize, saying Mr. Trump has survived so many would-be gaffes that would have doomed other candidates that they no longer know how to rate his chances now.

Indeed, there’s a sense that despite the near-universal condemnation from Republicans and Democrats in Washington, Mr. Trump could emerge more popular than ever with his enthusiastic supporters — though he may have put a ceiling on his ability to move beyond that base of support.

“I don’t think it affects the core group of people that are supporting Trump — not one iota,” said Henry Barbour, a member of the Republican National Committee from Mississippi. “Does it affect his ability broaden his support and win the nomination? Absolutely.”

Mr. Trump on Monday shocked the political world by saying he wanted to see a “complete and total shutdown” on Muslims entering the U.S. until concerns about terrorism can be addressed.

Most of his fellow candidates quickly moved to blast him, with several saying he’s shown he’s unfit for the White House and would be trounced by a Democrat.

But Mr. Cruz offered more muted criticism, passing on the chance to level a personal attack at Mr. Trump and focusing instead on his push to grant governors the power to stop refugee resettlement in their states and to enact a three-year moratorium on refugees coming here from Iraq, Syria and other terrorist infested countries.

“I disagree with that proposal,” Mr. Cruz told reporters, in response to a question about the Trump plan. “I like Donald Trump. A lot of our friends here have encouraged me to criticize and attack Donald Trump. I am not interested in doing that.”

David Johnson, a Georgia-based GOP strategist, said he is undecided on whether all the hoopla over Mr. Trump’s plan will reshape the race, but said Mr. Cruz decision not to attack Mr. Trump makes sense.

“I think it is smart because he is banking on Trump collapsing and inheriting his supporters,” Mr. Johnson said. “Cruz can appeal to the Trump constituency without going all the way overboard as Trump does, and he has the organization, and he is anti-establishment.”

Mr. Johnson said Mr. Cruz could the sole candidate in the race who is positioned to “inherit Trump’s endorsement” should Mr. Cruz outlast him in the race.

The political relationship between Mr. Cruz and Mr. Trump has been an intriguing subplot of the 2016 Republican race. Mr. Trump has tangled with just about everyone one of his rivals — with the exception of Mr. Cruz, who appeared to be positioning himself as a viable alternative should Mr. Trump drop out or his backers decide they want to look for another candidate.

Larry Sabato, of the University of Virginia’s Center for Politics, said that it is “exceedingly” unlikely that Mr. Trump will drop out and said “Trump’s backers are applauding, not booing” his Muslim plan.

“The establishment candidates are hurling brickbats at Trump not in the hope they can grab some of his base, but rather to seek to become his leading mainstream opponent,” Mr. Sabato said.

Michael Dennehy, a New Hampshire-based GOP strategist, said Mr. Trump’s “support comes from a very unique set of voters and there is no doubt in my mind that what he said about Muslims yesterday will have zero impact on his poll numbers — not in the least.”

Polls show Mr. Trump is the most divisive figure in the field, but his supporters are loyal.

Mr. Trump led the pack in a USA Today/Suffolk University Poll released Tuesday that also showed that 68 percent of his supporters plan to support him if he ditches the Republican Party and runs as an independent.

Surveys show voters are attracted to Mr. Trump’s blunt style and the sense that he has the strongest leadership qualities within the crowded GOP field.

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