Until now, Mr. Biden, Speaker Nancy Pelosi of California and Senator Chuck Schumer of New York, the Democratic leader, have insisted that Republicans agree to a spending bill of $2 trillion or more, while Senator Mitch McConnell of Kentucky, the majority leader, wants a much smaller package. The resulting impasse has threatened to delay additional economic aid until after Mr. Biden’s inauguration on Jan. 20.

Many of the president-elect’s advisers have become convinced that deteriorating economic conditions from the renewed surge in Covid-19 infections and the looming threat of millions of Americans losing jobless benefits in December amid a wave of evictions and foreclosures require more urgent action before year’s end. That could mean moving at least part of the way toward Mr. McConnell’s offer of a $500 billion package.

But top Democrats remain publicly adamant that Republicans need to move closer to their opening offer of $2.4 trillion. Mr. Biden, Ms. Pelosi and Mr. Schumer have given no public indication of how much they are willing to scale back their ambitions in order to reach a deal with Mr. McConnell, arguing that the Republican leader has not been willing to compromise.