Is Donald Trump considering wavering on a key campaign promise?

That's what several news reports published over the weekend suggest. And while the Trump campaign issued a statement denying any shift on immigration policy, top surrogates and campaign operatives hinted that a change just might be on its way.

The issue: what to do with the estimated 11 million immigrants already living in the United States illegally.

Since he entered the presidential race last year, Trump insisted they would have to be expelled from the country, despite the logistical and humanitarian questions a mass deportation would present.

"You're going to have a deportation force, and you're going to do it humanely," he told MSNBC in November 2015.

But this weekend, Buzzfeed reported that during a meeting with a Hispanic advisory council, Trump hinted he wasn't totally attached to that proposal. People who attended the meeting told the website that Trump asked for suggestions on a "humane and efficient" way to address people already living in the country illegally. Other news outlets confirmed the conversations.

Univision went one step further, reporting that Trump will roll out a new immigration plan Thursday in Colorado "that will include finding a way to legalize millions of undocumented immigrants."

That's something the campaign immediately pushed back on. "Mr. Trump said nothing today that he hasn't said many times before, including in his convention speech," said Trump campaign staffer Steven Cheung in a statement provided to NPR.

And yet, when asked on CNN the next day whether Trump's immigration policies would include that promised "deportation force," Trump's new campaign manager, Kellyanne Conway, responded, "To be determined."

On CBS News' Face the Nation, Alabama Sen. Jeff Sessions said Trump is "wrestling with how to do that," referring to removing people in the country illegally.

"He did not make a firm commitment yesterday or at the meeting the other day about what he will do with that," Sessions said. "But he did listen, and he's talking about it."

A major shift on immigration policy would be the clearest signal yet that, faced with widening deficits in most national and state-level polls, the Trump campaign is now making a concerted effort to appeal to moderate and independent voters.

But a shift would carry major political risks, too. Immigration is a key issue — if not the key issue — for many of Trump's fiercest supporters. And it's been a hallmark of Trump's campaign since day one, when he warned that people entering the country from Mexico were "bringing drugs; they're bringing crime; they're rapists."

Trump has also framed himself as a no-apologies "truth" teller, who will push for what he thinks is best regardless of the political consequences. Walking back from a high-profile promise could undermine that image.

Trump's campaign never provided details about what that deportation force would look like or how it would track down and expel people in the country illegally. But Trump stuck to the promise.

"We have no choice if we're going to run our country properly and if we're going to be a country," he said in a December debate.

Ohio Gov. John Kasich questioned Trump's proposal during that forum, saying, "Come on, folks. We all know you can't pick them up and ship them across — back across the border. It's a silly argument. It's not an adult argument. It makes no sense."

Trump responded by citing a controversial Eisenhower administration initiative called "Operation Wetback," which deported up to 1.5 million immigrants who were living in the United States illegally.

Trump's response to terrorism has centered on immigration as well. After the mass shootings at Orlando's Pulse nightclub in June, Trump reiterated his call for a temporary ban on all Muslims immigrating to the United States. That's despite the fact that the shooter was born in New York City.

"The only reason the killer was in America in the first place is because we allowed his family to come here," Trump said in his first speech after the attacks. "That is a fact — and a fact we need to talk about."

At nearly every campaign rally, supporters chant "Build that wall! Build that wall!" referencing Trump's promise to erect a wall along the entirety of the United States-Mexico border.

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