WASHINGTON — Optimism about delivering long-sought COVID-19 relief is building on Capitol Hill after additional rank-and-file lawmakers voiced support for a bipartisan, middle-of-the-road plan taking shape in the Senate and as top congressional leaders connected on the topic for the first time in months.

House Speaker Nancy Pelosi and Senate Majority Leader Mitch McConnell — frequent rivals but proven dealmakers — spoke on the phone Thursday, a conversation that came the day after Pelosi signaled a willingness to make major concessions in search of a COVID rescue package in the $1 trillion range.

Pelosi’s spokesman announced the telephone conversation, tweeting that it was “about their shared commitment to completing an omnibus and COVID relief as soon as possible.” McConnell’s office would not comment.

With COVID-19 caseloads spiraling and the daily death toll equaling records, the momentum for finally passing a second major relief bill is undeniably building, especially after President-elect Joe Biden and top congressional Democrats endorsed a $908 billion bipartisan framework to build an agreement.

Some conservatives, including Republicans from COVID hotspots like North Dakota and Iowa, said they were comfortable with an aid package carrying the almost $1 trillion price tag. Sen. Kevin Kramer, R-N.D., said the bipartisan plan is “the right balance of compromise and it’s a number that’s doable.”

Added Lindsey Graham, R-S.C.: “There’s a bipartisan package for $908 billion that will really help people.”

The path forward is cluttered with obstacles, however, including a tight time window and hard feelings from months of futile talks and a poisonous election. But the $908 billion cost is what many Republicans, McConnell included, signaled they were willing to accept this summer.

McConnell, R-Ky., his leverage bolstered after the election, continues to take a hard line, insisting in a Thursday floor speech that any relief package be limited to consensus items like another round of “paycheck protection” aid to businesses, funding to distribute vaccines, and aid to schools.

“Why should these impactful and noncontroversial life-preservers be delayed one second longer?” McConnell said. “At long last, let’s do what Congress does when we want an outcome. Let’s make law on all the subjects where we agree.”

A Huge Drop in Democratic Demands

Later, McConnell met with Republicans who are working the scaled-back, bipartisan measure, including Susan Collins, R-Maine, Lisa Murkowski, R-Alaska, and Mitt Romney, R-Utah. Across Capitol Hill, an allied bipartisan “problem solvers” group claimed growing momentum at an outdoor news conference.

A key McConnell ally, Sen. John Cornyn, R-Texas, said he is negotiating with fellow Judiciary Committee member Dick Durbin, D-Ill., over a provision much sought by Republicans and McConnell in particular that would give a liability shield to businesses, universities and other organizations against COVID-related lawsuits.

McConnell himself said a huge drop in Democratic demands — from more than $2 trillion to less than $1 trillion — was “at least movement in the right direction.”

And Trump weighed in to support the idea. Obtaining his necessary signature can be a bit of a high-wire act, especially since any COVID relief is likely to be added to a catchall spending bill.

“I think they are getting very close and I want it to happen,” Trump said.

At stake is whether to provide at least some COVID aid now rather than wait until Biden takes office. Businesses, especially airlines, restaurants and health providers, are desperate for help as caseloads spiral and deaths spike. Money to help states distribute vaccines is needed, and supplemental pandemic unemployment aid that provides additional weeks of jobless benefits expires at the end of the month.

Biden is supporting an additional aid package that’s as large as possible now. He said Wednesday that an aid package developed by moderates “wouldn’t be the answer, but it would be the immediate help for a lot of things.” He wants a relief bill to pass Congress now, with more aid to come next year.

Biden’s remarks followed an announcement by Pelosi, D-Calif., and Senate Democratic leader Chuck Schumer of New York supporting the almost $1 trillion approach as the “basis” for discussions. The announcement appeared aimed at budging McConnell, who so far has been unwilling to abandon a $550 billion Senate GOP plan that failed twice this fall.

The Democrats embraced the $908 billion approach from moderate Sens. Collins and Joe Manchin, D-W.Va., among others. It would establish a $300 per week jobless benefit, send $160 billion to help state and local governments, boost schools and universities, revive popular “paycheck protection” subsidies for businesses, and bail out transit systems and airlines.

The New Plan Includes a Liability Shield for Businesses

“In the spirit of compromise we believe the bipartisan framework introduced by Senators yesterday should be used as the basis for immediate bipartisan, bicameral negotiations,” Pelosi and Schumer said. They said they would try to build upon the approach, which has support in the House from the bipartisan “problem solvers” coalition.

The statement was a significant concession by Pelosi and Schumer, who played hardball this fall during failed preelection discussions with the administration on a costlier bill. They wanted a more generous unemployment benefit and far more for state and local governments. Their embrace of the $908 billion measure was a retreat from a secret $1.3 trillion offer the two Democrats gave McConnell just on Monday.

“In the spirit of compromise, Speaker Pelosi and I believe that the bipartisan framework introduced on Tuesday should be used as the basis, as a framework for immediate bipartisan negotiations,” Schumer said. “Of course, we and others will offer improvements but we believe with good faith negotiations we could very well come to an agreement.”

The new plan includes a liability shield for businesses and other organizations that have reopened their doors during the pandemic. It’s the first time Pelosi and Schumer have shown a willingness to consider the idea, a top priority of McConnell, and Durbin’s involvement suggests a level of seriousness that had not been previously seen.

McConnell had dismissed the bipartisan offer on Tuesday, instead aiming to rally Republicans around the $550 billion GOP proposal. But McConnell himself endorsed a $1 trillion-or-so plan this summer, only to encounter resistance from conservatives that prompted him to retrench. He has acknowledged that another infusion of aid to states and local governments, a key Pelosi demand, probably will pass eventually.

McConnell wouldn’t respond when asked about the Democratic statement. His top deputy, Sen. John Thune, R-S.D., said GOP leaders might agree to merging the bipartisan proposal with McConnell’s bill.

“I think there’s still time, although it’s short, to put a bill together,” Thune said Wednesday.

Any relief package would be attached to a $1.4 trillion year-end spending bill required to avert a government shutdown next weekend. Talks on that measure are proceeding, but if lawmakers should stumble, a temporary spending bill would be needed as a bridge into next year.