"I've got you covered," Mr. Trump added, reinforcing the thought that he might take the option of declaring a national emergency under existing law, and move to shift money around in the budget to fund construction of a border wall.
A deal on border security funding must be reached by February 15, or there is a risk of a second partial government shutdown.
President Trump's tweets came after House Democrats unveiled the outlines of a border security funding plan which included no direct provision for border barriers - whether they are described as fencing or walls.
"We will push for a smart, effective border security posture, one that does not rely on costly physical barriers," Democrats wrote.
You can see the full plan from Democrats here.
It wasn't immediately apparent if Democrats would be open to a compromise which included some border security funding - or if the President would simply use the 'national emergency' declaration in an effort to fund those priorities.
In Congress, lawmakers on the House-Senate panel tasked with negotiating a deal said it was time to forge a compromise.
"It means by definition, nobody gets everything they want," said Sen. Roy Blunt (R-MO).
"Compromise means both sides have to get something they need, right?" asked Sen. John Hoeven (R-ND).
"We certainly have a lot of work to do," said Sen. Jon Tester (D-MT).
In one of his social media posts on Thursday morning, the President again tweeted that the wall is already being built along the Mexican border - that is not true; no new sections of border barrier have been funded and constructed during his two years in office.
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