President Donald Trump Sunday raised the possibility of amnesty for  hundreds of thousands of undocumented migrants who came to United States as children, a move that could further rankle his conservative base.

The announcement, via Twitter, comes a day after far-right groups panned immigration policy changes he proposed as a way out of the partial government shutdown.

“No, Amnesty is not a part of my offer. It is a 3 year extension of DACA,” Trump tweeted in response to the proposal he unveiled Saturday afternoon, which drew howls from conservatives. “Amnesty will be used only on a much bigger deal, whether on immigration or something else.”

On Saturday, the president offered three-year extensions of two immigration programs important to Democrats in exchange for his $5.7 billion demand for border wall funding. The border structure is the sticking point in getting 800,000 furloughed federal employees back to work as his stalemate with Democrats — approaching a month in length — continues.

[ANALYSIS | White House flashes urgency on shutdown — but actual goal is murky]

Trump as a 2016 presidential candidate ran, in large part, on a hardline immigration agenda that included a wall and calls to find and deport millions in the country illegally. Positioning himself with hardliners, and the promises he made to conservative voters, were both parts of what led him to help nix a bipartisan Senate immigration reform bill last year.

Sen. Mark Warner, D-Va., said President Trump’s new proposal for a border security plan could serve as a “starting point” for negotiations if the shutdown were brought to an end.

“I’ll use that as a starting point, but you’ve got to start by opening the government,” Warner said on NBC’s “Meet the Press” program Sunday.

“We cannot reward the kind of behavior of hostage-taking,” Warner said. “If the president can arbitrarily shut down the government now, he will do it time and again.”

Watch: Remember When Donald Trump Wanted Mexico To Pay for the Wall?

In another move likely to further frustrate conservative groups and lawmakers, the president signaled Sunday that he would not insist that any future potential immigration reform measure include funds or a plan to find and deport most of those in the country illegally.

“Likewise there will be no big push to remove the 11,000,000 plus people who are here illegally-but be careful Nancy!” Trump wrote in a murky message to Speaker Nancy Pelosi, D-Calif.

No, Amnesty is not a part of my offer. It is a 3 year extension of DACA. Amnesty will be used only on a much bigger deal, whether on immigration or something else. Likewise there will be no big push to remove the 11,000,000 plus people who are here illegally-but be careful Nancy!

— Donald J. Trump (@realDonaldTrump) January 20, 2019

The Pew Research Center found there were 10.7 million undocumented migrants illegally in the United States in 2016. That was a dip from a high of 12.2 million nine years earlier.

Shortly after Trump spoke on Saturday, he began taking flack from his conservative base.

James Carafano, a vice president of the conservative Heritage Foundation said Saturday the president should “be applauded” for trying to end the shutdown, before ripping into his latest plan toward doing so.

“However, including amnesty in the new proposal is not the way to do it. Amnesty encourages further illegal immigration, incentivizes the tragedy of human trafficking, and undermines our citizens’ confidence in the rule of law,” Carafano said.

 [Trump offers trade of Dreamers-for-wall that Democrats quickly reject]

“Unlike many in Washington, President Trump has shown himself to be serious about securing the border and fixing our broken immigration system. For this he is to be commended,” the Heritage VP said. “However, the proposed compromise is not the best way forward.”

Vice President Mike Pence, in a roundtable session Saturday with a group of reporters after Trump’s remarks, tried to assuage any reluctant Republicans and reach out to needed Democrats.

“There is no amnesty in the president’s proposal. There is no pathway to citizenship in this proposal. It’s three-year relief for TPS and DACA,” Pence said. “We’re going to work hard and reach across the aisle.”

Conservative commentator William Kristol, a frequent Trump critic, pounced on Trump’s amnesty embrace, suggesting it could draw a 2020 primary challenger from the GOP’s far right — then making Trump vulnerable to a more moderate Republican challenger.

“Amnesty will be used only on a much bigger deal, whether on immigration or something else.” Excellent. The chances of a Tom Tancredo/Steve King-type challenge go up, which will make Trump even more vulnerable to the real alternative, a challenger from the sane wing of the GOP. https://t.co/ju0P0b5pbm

— Bill Kristol (@BillKristol) January 20, 2019

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Trump’s Sunday morning tweet, and its embrace of amnesty, came after some notable conservatives blasted him Saturday for what would only be temporary extensions of programs providing protections for those here illegally. 

Trump proposes amnesty. We voted for Trump and got Jeb!

— Ann Coulter (@AnnCoulter) January 19, 2019

A Big Beautiful Concrete Border Wall will be a monument to the Rule of Law, the sovereignty of the USA, & @RealDonaldTrump. If DACA Amnesty is traded for $5.7 billion(1/5 of a wall), wouldn’t be enough illegals left in America to trade for the remaining 4/5. NO AMNESTY 4 a wall!

— Steve King (@SteveKingIA) January 19, 2019

The conservative reaction is ratcheting up. Here’s https://t.co/X1Hv5cJ6hJ‘s new headline: Three Year Amnesty, Most of the Border Remains Open pic.twitter.com/5KWa2CLcDM

— Michael D. Shear (@shearm) January 19, 2019