The four congressional leaders have agreed that any additional pandemic aid should be wrapped into the year-end spending measure, and that Congress should not adjourn without approving some pandemic relief as Covid-19 cases continue to rise across the country and the government works to distribute the vaccine to essential workers and others. “We’re going to get an agreement as soon as we can agree,” Mr. McConnell told reporters after the first meeting.

Aides involved in the discussion said they were nearing agreement on a catchall spending package, and the text could be released as early as Wednesday. But it remained unclear what congressional leaders would agree to for pandemic relief, as well as what additional legislative items may be merged with the broader spending package.

Even if Congress were to pass a bill this week, it may not be in time to prevent millions of Americans from going weeks with no source of income, given that many state unemployment offices have already programmed their systems to cut off benefits after next week, when the current pandemic programs expire.

Reinstating the benefits in those states will take time, especially because the plan being considered by Congress would make several technical changes to the programs, which the Labor Department must then incorporate into formal regulations, said Elizabeth Pancotti, a policy adviser for Employ America, an advocacy group. The Christmas and New Year’s holidays, when state offices are shut, will add further delays, she warned, though workers would eventually receive back pay for the weeks where their benefits lapsed.

There are still hurdles to a final agreement, particularly without a bipartisan consensus on the two thorniest policy impediments: a Democratic demand for additional aid to support state and local governments and a Republican push for sweeping liability protections for businesses, hospitals, schools and other institutions open during the pandemic.