Senate Majority Leader Mitch McConnell quickly praised the deal and said he was ready to bring the measure to the floor, but it's already clear that Democrats are uninterested.
"This senseless government shutdown is hurting millions of Americans, and its impacts are only getting worse".
He said his opponents "don't see crime and drugs, they only see 2020 - which they are not going to win".
Pointedly ignoring his personal comments, Pelosi on Twitter emphasised the need to end the partial government shutdown, which has inflicted increasing pain around the country as it entered its 30th day.
She said the State Department told her "the president outing" the original trip made the scene on the ground in Afghanistan "more risky because it's a signal to the bad actors that we're coming". "Wall!" at his arena rallies has swayed Trump before, including a year ago, when the conservative news site Breitbart branded him "Amnesty Don" for considering a similar deal that would have provided $25 billion in wall funding for a path to legal status for those the DACA program was created to help.
Still, TSA reports that, on Saturday, 99.9 percent of passengers waited less than 30 minutes and 93.8 percent waited less than 15 minutes.
Trump is seeking $5.7 billion for border-wall funding. He's referring to House Speaker Nancy Pelosi, who rejected his proposal to trade wall money for temporary protections for some immigrants. Right-wing commentator Ann Coulter tweeted: "Trump proposes amnesty". "Amnesty will be used only on a much bigger deal, whether on immigration or something else", he added.
Sunday morning, Trump suggested he may even be willing to consider a blanket "amnesty" for illegal immigrants living inside the United States, but only in return for a "bigger deal".
But Trump's proposal to end the 29-day partial shutdown of the U.S. government, which was sparked by a dispute over funding for the wall, appeared dead on arrival, with the top Democrat in Congress rejecting the proposal based on reports of its contents prior to the speech.
"This is a common-sense compromise both parties should embrace", Trump said.
Sen. Blackburn, who champions Trump's America First agenda in Congress, said that we must deliver for the American people and the border patrol agents by securing the southern border.
Watch: Remember When Donald Trump Wanted Mexico To Pay for the Wall?
"I will be making a major announcement concerning the Humanitarian Crisis on our Southern Border, and the Shutdown", Mr. Trump tweeted Friday evening.
On Saturday, Trump said Pelosi "is under total control of the radical left".
Democrats, however, criticized Trump's proposal for failing to offer a permanent solution for the immigrants in question and because he refuses back away from his demand a wall along the U.S. -Mexico border, which the party strongly oppposes.
Workers have now missed one paycheck and will miss another if the shutdown is not resolved in the next week.
Administration officials said the protections would apply only to those now in the Obama-era program shielding them from deportation, and the temporary protected status would apply to those who now have it and have been in the USA since 2011. Now, President Trump is offering Speaker Pelosi and the Democrats a top legislative priority of theirs in an effort to end this partial government shutdown. And Lisa Murkowski of Alaska, another key centrist, said she would study the details of the plan but did not commit to vote for it. She isn't saying whether she'd vote for it.
The partial government shutdown, which marks the longest lapse in funding in modern USA history, is now in its 29th day as the stalemate over the funding of the border wall persists.
"In a very real sense, what President Trump did here was he set the table for a deal", Pence said on "Fox News Sunday".
"The way to end this shutdown is for both sides to make mutual concessions in order to reach an agreement".