"This is a common sense compromise both parties should embrace," the President added in his remarks from the White House.
"Everyone has made their point — now it’s time to make a law," said Senate Majority Leader Mitch McConnell. "I intend to move to this legislation this week."
The plan offered by the President has two main compromise items, one is a bipartisan legislative effort known as the "BRIDGE ACT" - would only be a temporary solution for those known as "Dreamers" - offering them a three-year protected status in the United States, but not resolving any question about a longer-term pathway to U.S. citizenship.
The President is also offering to extend protections for certain immigrants and refugees who have come to the U.S. under a "Temporary Protected Status" or TPS, and have remained in the United States longer than originally envisioned.
That's a change from last year, when the Trump Administration moved to send back thousands of people to their home countries - Nicaragua, Haiti, El Salvador, and Sudan - ending an extended temporary protection for those who had come to the United States - but a federal court put that move by the President on hold in October.
It was the first major offer made by the President since this impasse began before Christmas, as Mr. Trump had previously waved off efforts by some GOP lawmakers to add provisions dealing with DACA and other programs which helped illegal immigrants in the United States.
But his Saturday speech did little to sway Democratic leaders in Congress.
"It is unlikely that any one of these provisions alone would pass the House, and taken together, they are a non-starter," said House Speaker Nancy Pelosi, as she and other Democrats said the immigration offers were temporary, while the wall was permanent.
"Unfortunately, the president doesn’t understand that an honest negotiation can’t take place while he’s holding the government hostage," said Rep. Lucille Roybal-Allard (D-CA).
"You don’t negotiate a compromise with your own Vice President and your son in law," said Sen. Brian Schatz (D-HI), as Democrats noted there have been no direct talks in almost two weeks. "That’s not how this works."
"No genuine path to citizenship for dreamers, more intransigent insistence on an ineffective, impractical wall—nothing new from Trump today," said Sen. Richard Blumenthal (D-CT).
Republicans said the Democrats should accept the President's offer, as both sides pointed the shutdown finger of blame at each other on the 29th day of the border security impasse, which began back before Christmas, when Republicans controlled both the House and Senate.
"The President has made a very reasonable offer to extend DACA and TPS protections in exchange for the border security measures he supports," said Sen. Marco Rubio (R-FL).
"Democrats have yet to make a single legitimate counteroffer throughout the last month the government has been shut down," said Rep. Steve Scalise (R-LA).
"This is an important step in the right direction to restart negotiations," said Rep. Elise Stefanik (R-NY), who has broken repeatedly with GOP leaders and the White House to vote for Democratic plans to re-open the government.
Mr. Trump's plan also includes:
+ $800 million in humanitarian aid to deal with an influx of illegal immigrants
+ $805 million for drug detection efforts at major ports of entry
+ 2,750 new border agents and other law enforcement personnel
+ 75 new legal teams of immigration judges
The President said the three year temporary legal status would help about 700,000 Dreamers, while the extended TPS status would help about 300,000 others.
But the plan also ran into opposition from some voices on the conservative right as well.