“I feel optimistic that there is a light at the end of the tunnel,” Speaker Nancy Pelosi, Democrat of California, said after hosting another round of talks in her Capitol Hill office with Steven Mnuchin, the Treasury secretary; Mark Meadows, the White House chief of staff; and Senator Chuck Schumer, Democrat of New York, the minority leader. “But how long that tunnel is remains to be seen,” Ms. Pelosi added.

On the Senate floor, Mr. Schumer called for the Postal Service to fix mail delays that have resulted from cutbacks that Postmaster General Louis DeJoy put in place during the pandemic. Democrats and voting rights groups have charged that the cuts are part of a deliberate effort by President Trump to undermine the service in order to interfere with mail-in voting that will be critical to a safe election in November. Democrats have called for $3.6 billion in the aid package to ensure a secure election, including broader mail balloting, but Republicans are opposing the funds.

Other outstanding disputes include whether to appropriate hundreds of billions of dollars to help states and local governments avoid laying off public workers as tax revenues fall, and whether to reinstate a $600 per week unemployment supplement from the federal government to laid-off workers.

Democrats are pressing to extend the payments, which lapsed last week, through January. Republicans on Tuesday countered with a plan to resume them at $400 per week through Dec. 15, according to two people with knowledge of the discussions who insisted on anonymity to describe them. Democrats declined the offer, they said.

“There are no top-line numbers that have been agreed to,” Mr. Meadows, the White House chief of staff, said after the Capitol Hill meeting, charging that Democrats were unwilling to make significant concessions. “We continue to be trillions of dollars apart in terms of what Democrats and Republicans hopefully will ultimately compromise on.”