Trump also underlined in his speech that he was making his pitch to "break the logjam" that has paralyzed Washington since late December, leaving roughly a quarter of the government closed and forcing roughly 800,000 federal employees be furloughed or work without pay. "The president has offered a compromise and the Democrats are refusing to go there", King said in an interview on the Cats Roundtable radio show.
The proposals were meant to be sweeteners for Democrats, though many in Congress have called for permanent solutions on both issues.
Roy Beck, president of NumbersUSA, which seeks a reduction in immigration, said Trump has forgotten the American workers who were central to his campaign promises.
Tensions flared when Pelosi suggested Trump postpone the annual State of the Union address, a grand Washington tradition - and a platform for his border wall fight with Democrats - that was tentatively scheduled for January 29.
They said they made a decision to talk to the back-benchers to try to break the gridlock left when House Speaker Nancy Pelosi told Mr. Trump at a meeting earlier this month she would never entertain any border wall money.
In exchange, he asked for $5.7 billion for building sections of a "see-through wall" on the Mexico border - a request which Congressional Democrats earlier rejected.
The president also called for $800 million in "urgent humanitarian assistance" and $805 million for drug detection technology to help secure United States ports of entry.
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.
In a briefing for reporters after Trump's remarks, the aides acknowledged that the bill faces a hard path in the Senate, where it would require 60 votes to overcome a filibuster.More news: David Warner to return to Australia after injuring elbow in Bangladesh
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.
Pelosi said the offer was a "non-starter" that did "not represent a good faith effort to restore certainty to people's lives".
Hard-line immigration proponents, including conservative columnist Ann Coulter, mocked Trump for the Dreamers deal.
The White House has billed Trump's plan as an attempt to end the shutdown.
Besides the 700,000 immigrants already enrolled in the so-called DACA or "Dreamers" program, Trump's proposal would also extend to another 300,000 people who had been protected from deportation under another program. The president's tweet also suggested he would not insist on finding and deporting migrants who are in the country illegally.
The question now is, what will House Speaker Nancy Pelosi, Senate Minority Leader Chuck Schumer, Senate Majority Leader Mitch McConnell and House Minority leader Kevin McCarthy do?
Trump's Friday evening tweeted announcement came after Pelosi, D-Calif., on Friday canceled her plans to travel by commercial plane to visit USA troops in Afghanistan, saying Trump had caused a security risk by talking about the trip.
"Border security and investing in keeping us safe is a better way to talk about it because a wall is a waste of money and will not actually help us create safety", she added.
"This week", he continued, "we received proof the administration planned months in advance to separate thousands of children from their parents and jail them as a deterrence to stop immigrants from seeking refuge in the U.S. Children have died while in U.S. custody; some have been tear-gassed by U.S. border agents; asylum seekers are being denied access to the legal system to apply".
Sen. Kirsten Gillibrand, D-N.Y., who is pursuing a 2020 presidential bid, said on CNN's "State of the Union" that her counter-offer to Trump would be "what we put on the table a year ago and voted for, which was to protect all dreamers". It's three-year relief for TPS and DACA.