WASHINGTON >> A group of Senate Republicans called on President Joe Biden to meet them at the negotiating table as the newly elected president signaled he could move to pass a new $1.9 trillion coronavirus aid package with all Democratic votes.

Ten Senate Republicans wrote Biden in a letter released today that their smaller counterproposal will include $160 billion for vaccines, testing, treatment and personal protective equipment and will call for more targeted relief than Biden’s plan to issue $1,400 stimulus checks for most Americans.

“In the spirit of bipartisanship and unity, we have developed a COVID-19 relief framework that builds on prior COVID assistance laws, all of which passed with bipartisan support,” the Republican lawmakers wrote. “Our proposal reflects many of your stated priorities, and with your support, we believe that this plan could be approved quickly by Congress with bipartisan support.”

The call on Biden to give bipartisanship negotiations more time comes as the president has shown signs of impatience amid growing calls from the more liberal wing of his party to pass his $1.9 trillion legislation through budget reconciliation, a process that would allow him to move the massive bill with only the support of his Democratic majority.

The Republican lawmakers did not provide many details of their proposal. One of the signatories, Louisiana Sen. Bill Cassidy, said that their package would cost a fraction, about $600 billion, of the Biden plan.

Winning the support of 10 Republicans would be significant for Biden. If all Democrats were to support an ultimate compromise bill, the legislation would reach the 60-vote threshold necessary to pass legislation under regular Senate procedures.

“If you can’t find bipartisan compromise on COVID-19, I don’t know where you can find it,” said Ohio Sen. Rob Portman, who also signed the letter.

The other GOP senators pushing the effort are Susan Collins of Maine, Lisa Murkowski of Alaska, Mitt Romney of Utah, Shelley Moore Capito of West Virginia, Todd Young of Indiana, Jerry Moran of Kansas, Mike Rounds of South Dakota, and Thom Tillis of North Carolina.

Brian Deese, the top White House economic adviser who has been leading the administration’s outreach to Congress, said administration officials were reviewing the letter. He did not immediately commit to Biden meeting with the lawmakers.

Deese signaled the White House could be open to negotiating with Republicans on their proposal on further limiting who would receive stimulus checks. Portman suggested today that the checks should be limited to individuals who make no more than $50,000 per year and families who make $100,000 per year.

Under the Biden plan, families with incomes up to $300,000 could receive some stimulus money.

“That is certainly a place that we’re willing to sit down and think about, are there ways to make the entire package more effective?” Deese said.

As a candidate, Biden predicted his decades in the Senate and his eight years as Barack Obama’s vice president gave him credibility as a deal maker and would help him bring Republicans and Democrats to consensus on the most important matters facing the country.

But less than two weeks into his presidency, Biden showed frustration with the pace of negotiations for relief at a time when the economy is showing further signs of wear from the pandemic. Last week, 847,000 Americans applied for unemployment benefits, a sign that layoffs remain high as the coronavirus pandemic continues to rage.

“I support passing COVID relief with support from Republicans if we can get it. But the COVID relief has to pass — no ifs, ands or buts,” Biden said on Friday.

In the letter, the Republican lawmakers reminded Biden that in his inaugural address, he proclaimed that the challenges facing the nation require “the most elusive of things in a democracy: Unity.”

Cassidy separately criticized the current Biden plan as “chock-full of handouts and payoffs to Democratic constituency groups.”

“You want the patina of bipartisanship … so that’s not unity,” Cassidy said.

Jared Bernstein, a member of the White House Council of Economic Advisers, said that Biden remains willing to negotiate but that White House officials needed to see more details from Republicans about their plan. At the same time, Bernstein pressed the Biden administration’s argument that doing too little to stimulate the economy could have enormous impact on the economy in the near and long-term.

“Look, the American people really couldn’t care less about budget process, whether it’s regular order, bipartisanship, whether it’s filibuster, whether it’s reconciliation,” Bernstein said. “They need relief, and they need it now.”

Both Portman and Deese spoke on CNN’s “State of the Union.” Cassidy and Bernstein spoke on “Fox News Sunday.”