WASHINGTON (AP) — Top negotiators reported at least some progress on a long-delayed COVID-19 aid package Tuesday after a rare meeting of Capitol Hill’s four most senior lawmakers. The quartet, including House Speaker Nancy Pelosi and top Senate Republican Mitch McConnell, said they would reconvene Tuesday night in hopes of sealing an agreement soon.

“I think there’s progress,” reported House Minority Leader Kevin McCarthy, R-Calif., as he left the session in Pelosi’s office. Treasury Secretary Steven Mnuchin joined by phone.

The uptick in activity could be a sign that an agreement is near, though COVID-19 relief talks have been notoriously difficult and Pelosi continues to press for help for states and local governments whose budgets have been thrown out of balance by the pandemic. GOP leaders oppose the idea and say it’s the biggest sticking point from their perspective.

A top GOP negotiator said the leaders had essentially agreed to agree.

“We are still talking to each other and there is agreement that we are not going to leave here without the omni and the COVID package,” said McConnell, R-Ky., using Capitol Hill’s shorthand for a catchall, omnibus spending bill that would be paired together with the COVID relief measure and a variety of other end-of-session items.

The Kentucky Republican is playing a strong hand in the lame-duck session and is pressuring Democrats to drop a much-sought $160 billion state and local government aid package. Several senior Democrats, including close allies of President-elect Joe Biden — who is eager for an agreement — have said they would go along now and fight for the aid next year.

McConnell says he’ll drop a demand for provisions shielding businesses from COVID-19-related lawsuits, a key priority of McConnell. He is pressing a lowest-common-denominator approach that would drop the lawsuit shield idea for now if Democrats agree to drop the $160 billion state and local aid package.

“We can live to fight another day on what we disagree on,” McConnell said Tuesday. “But we ought to go forward with what we can agree on.”

Pelosi has insisted for months that state and local aid would be in any final bill, but as time is running out, Democrats appear unwilling to hold the rest of the package hostage over the demand.

“We’re not going home until this is done,” said Sen. Joe Manchin, D-W.Va., on CNN Tuesday morning. “We’ve got to get people a lifeline.”

Manchin is an architect of a bipartisan $748 billion aid package that is aimed at serving as a template for the leadership talks. Mnuchin supports a package with many similar elements, and any final deal is likely to contain money for struggling businesses, the unemployed, schools and vaccine distribution. There is also bipartisan support for transportation and transit assistance, funding for rural internet service, and help for the Postal Service, among other provisions.