President Trump, facing the threat of a government shutdown in two days, is expected to meet with the top congressional leaders in both parties at the White House on Monday afternoon as they clash over the terms of a deal to keep federal funds flowing.

Should the group fail to strike an agreement to extend spending and enact it into law within hours, the bulk of federal operations would come to a halt on Wednesday at 12:01 a.m., with broad consequences for the country.

Democrats have refused to agree to a stopgap measure offered by Republicans to extend federal funding into November, demanding that any spending legislation include additional money for health care programs to protect Americans from losing coverage. Without Democrats’ backing, Republicans, who have only a narrow majority in the Senate, cannot muster the 60 votes needed to push through an extension. But the G.O.P. has refused to agree to any concessions.

With the two parties at an impasse, Mr. Trump last week rejected the idea of striking a deal to win bipartisan support and canceled a meeting he had scheduled with the two top congressional Democrats, Senator Chuck Schumer and Representative Hakeem Jeffries, both of New York.

Monday’s meeting will be the first time in this term that Mr. Trump has invited the Democratic leaders to the White House, and the first time that Mr. Jeffries has ever met with him. It will come as the Senate returns from a weeklong recess in which no progress appears to have been made toward reaching a deal.

Leaders of both parties suggested on Sunday that they saw room to negotiate on their funding proposals, but they signaled skepticism that the meeting might result in a compromise.