The escalated push to get Trump's priorities, which Democrats reject, into spending legislation could jeopardize prospects for an agreement to keep the government open.
If talks fail, the government would shut down on Saturday, Trump's 100th day in office.
"Obamacare is in serious trouble. The Dems need big money to keep it going - otherwise it dies far sooner than anyone would have thought," the Republican president said in a Twitter post.
In a second tweet, he added: "The Democrats don't want money from budget going to border wall despite the fact that it will stop drugs and very bad MS 13 gang members."
MS-13 is a criminal gang with members of Central American origin.
The president's tweets appeared after White House budget director Mick Mulvaney accused Democrats of "holding hostage national security" by opposing $1.5 billion to help build a wall along the US-Mexico border, one of Trump's top campaign pledges.
Democrats have said they would not support legislation that ends federal subsidies to help low-income people buy health insurance under the Affordable Care Act, popularly known as Obamacare.
The healthcare law was former Democratic President Barack Obama's signature domestic policy achievement, which Republicans are trying to repeal and replace.
On Sunday, Democrats called for Trump to stop making "poison pill" demands.
Senate Democratic leader Chuck Schumer said negotiations between Democrats and Republicans in both the House of Representatives and the Senate were "going quite well" and that he was hopeful a deal could be reached.
"The only fly in the ointment is that the president is being a little heavy handed, and mixing in and asking for things such as the wall," Schumer told reporters.
"We'd ask him to let us do our work, not throw in some last-minute poison pills that could undo it, and we could get this done," he said.
Trump wants money for the wall included in spending legislation that Congress must pass by Friday to keep the federal government operating through Sept. 30, when the 2017 fiscal year expires.
Mulvaney and White House Chief of Staff Reince Priebus played down the danger of a shutdown. Mulvaney said talks between Republicans and Democrats could produce an agreement as early as Sunday.
"I'm pretty confident we're going to get something that's satisfactory to the president in regard to border security within the current negotiations," Priebus said on NBC's "Meet the Press."
Homeland Security Secretary John Kelly said Trump had been clear about his desire for a wall. "I would suspect he will be insistent on the funding," he told CNN's "State of the Union."
Tax reform: Principles but no plan
The White House is expected to address another Trump campaign promise this week with a Wednesday announcement on tax reform that Mulvaney said would offer "governing principles, some guidance, also some indication of what the rates will be."
But he said basic elements of the plan remained undecided, including whether to have deficit-funded tax cuts that would not be permanent. "You can either have a small tax cut that's permanent, or a large tax cut that is short term," he said.
In a tweet on Saturday, Trump promised that a "Big TAX REFORM AND TAX REDUCTION will be announced next Wednesday."
Legislative text on tax reform is not expected until June, Mulvaney said.
Spending legislation will require Democratic support to clear the Senate, and the White House says it has offered to include $7 billion in Obamacare subsidies to help low-income Americans pay for health insurance, if Democrats accept funding for the wall.
Democrats showed no sign of softening their opposition to wall funding on Sunday and sought to place responsibility for any shutdown squarely on Trump and Republicans who control the House of Representatives and the Senate.
"The Democrats do not support the wall," House Democratic leader Nancy Pelosi told NBC's "Meet the Press." "The wall is, in my view, immoral, expensive, unwise."
Senator Richard Durbin, an Illinois Democrat, called on Trump to "back off."
"To think that he would consider shutting down the government of the United States of America over this outlandish proposal of a border wall ... that would be the height of irresponsibility," he told CNN.
(Additional reporting by Valerie Volcovici)
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)