A day after offering Democrats a compromise designed to break an almost month-long impasse over border security funding, which has idled hundreds of thousands of federal government workers as a result of a partial government shutdown, President Donald Trump on Sunday denied that his plans amounted to 'amnesty' for illegal immigrants, as he pressed Democrats to accept the deal.

"Amnesty is not a part of my offer," the President wrote in one of a series of Sunday posts on Twitter about his Saturday afternoon speech, which basically offered temporary protection from deportation for about 1 million illegal immigrants, in exchange for $5.7 billion in funding for a border wall.

Mr. Trump also sought to put pressure on Democrats - especially House Speaker Nancy Pelosi, as the White House touted the support of Republicans in the Senate, who will try to advance the border plan later this week.

"Nancy Pelosi and some of the Democrats turned down my offer yesterday before I even got up to speak," the President said.

There were some conservative voices who gave the President's plan a thumbs-down, not pleased with the move to shield around 700,000 DACA recipients, and another 300,000 people who had overstayed their temporary permission to be in the U.S. - but Republicans in the Senate tried to make it look like those voices were a minority of the GOP.

"All members of Congress should take this proposal seriously," said Sen. David Perdue (R-GA).

"I will absolutely vote for this proposal," said Sen. Roger Wicker (R-MS).

The irony of the President's immigration proposals weren't lost on Democrats - as the Trump Administration has tried to end protections for DACA recipients, and targeted hundreds of thousands of others with "Temporary Protective Status" for deportation.

"The President cancelled DACA. He stopped TPS," said Rep. David Cicilline (D-RI). "He got us into this mess."

"Once again, Trump is trying to find leverage with problems that he created. No deal," said Rep. Earl Blumenauer (D-OR).

"Stop holding federal employees hostage and stop holding the young people in DACA hostage," said Sen. Bernie Sanders (I-VT).

As for the actual legislative details of the President's plan, those still weren't available on Sunday, but Politico reported that the plan may also include over $12 billion in hurricane and wildfire disaster relief, along with other spending provisions - all of that would need 60 votes to advance in the Senate.

The House and Senate are not in session on Monday, because of the federal holiday for Dr. Martin Luther King, Jr.

This was originally a legislative break week for Congress, but now will be ground zero for the fight over the border wall and the partial shutdown.

If no final deal is reached this week, 800,000 federal workers would miss a second paycheck on Friday, January 25.