Donald Trump's sudden signal that he's ready to soften his approach on immigration has split his backers, as some are cautiously supporting him, others are wary and some are outraged that he's moving away from the tough stance he outlined last year.

Trump told Fox News' Sean Hannity this week that he was open to allowing illegal immigrants to remain in the U.S., and said he would "work with" them. He hinted that they might be able to stay if they pay back taxes, although he said he would still kick the "bad ones" out, and said he would still build the border wall.

Still, those comments fly in the face of Trump's previous plan for a "deportation force" that would remove the 11 million illegal immigrants from the U.S., and it forced Trump supporters of all stripes to try to get their heads around the sudden change.

Sen. Jeff Sessions, the first U.S. senator to openly support Trump, said Thursday that he would be "supportive" of a potential deal on the issue. However, he noted that dealing with the 11 million will take a back seat to enforcement of the law in any deal.

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"The most important thing is to focus first and foremost on a lawful system that protects the interests of the American people first. If you enter the country unlawfully you're subject to being deported," Sessions said. He said he could "get on board" with that kind of proposal.

"Oh, yeah, I can be supportive of that," Sessions said. "But you have to be careful because you've got to have the rule of law ... Look I think that's some of the things that he just mentioned. He's not announced what he's going to do. And I'm giving you some of my opinions about how I think we ought to approach this serious problem of re-establishing the lawful system of immigration."

But some anti-immigration groups were skeptical of Trump's new take on the issue. Bob Dane, the executive director for the Federation for American Immigration Reform, warned Trump that if his shift lets some illegal immigrants to remain, that is essentially giving them amnesty.

"If Trump is noodling around exceptions or conditions that allow some or many to stay, he should know that any and all variations of requirements that might bestow work permits or citizenship to those who violate our laws constitutes amnesty," Dane told the Washington Examiner in a statement. "Voters know that the problem with amnesty is that it rewards illegal behavior ... It also sends the message that the punishment for entering our country illegally varies according to the political whims of the moment rather than the permanency of our INA (Immigration and Nationality Act) laws."

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Ann Coulter, author, Trump supporters and a leading anti-immigration voice, told the Washington Examiner that Trump's rhetorical change has her unnerved. She also openly worried earlier in the week that her current tour for her new book, "In Trump We Trust," could be undercut by the change.

"It mostly worries me rhetorically. … I mean, what to do with the illegals already here was never really a big part of it," she said, pointing to the wall Trump plans to build. "I don't think it is a change in policy ... The policy is anyone who's here illegally, is here illegally, does not have the right to be here. We'll decide whether it's in our interest to let them stay or not. Perhaps it is in our interest to let some of them stay."

Trump has also infuriated some of his supporters. Mark Krikorian, executive director of the Center for Immigration Studies, declared that Trump's latest remarks were the "last straw" for him, especially his statement that there would be "no amnesty," which he made just before saying that illegal immigrants will have to pay back taxes.

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"Those are terms of art in the pro-amnesty, Gang of Eight crowd. Every politician pushing an amnesty says 'this version isn't really an amnesty because fill in the blank,'" Krikorian said, declaring Trump the "unofficial ninth member of the Gang of Eight."

"What he just did was make clear that even on his central issue, which is the only reason he's the nominee ... was immigration, and he now has shown that he can't be relied on, even on that," Krikorian said, who had previously considered himself a reluctant Trump supporter — until now.

"I'm done with Trump at this point," he said.