WASHINGTON (AP) — Senate bargainers have reached agreement on a slimmed-down $10 billion package for countering COVID-19 with treatments, vaccines and other steps, but both parties' bargainers ended up dropping all funding to help nations abroad combat the pandemic.

Yet a day after lawmakers announced the bipartisan accord, it was possible the measure could get entangled with an election-year battle over immigration, and it was unclear Tuesday how quickly the bill might move through Congress.

The compromise drew quick support Monday from President Joe Biden, who initially pushed for a $22.5 billion package. In a setback, he ended up settling for much less despite administration warnings that the government was running out of money to keep pace with the disease's continued — though diminished — spread in the U.S.

"Every dollar we requested is essential and we will continue to work with Congress to get all of the funding we need," said White House press secretary Jen Psaki. "But time is of the essence. We urge Congress to move promptly on this $10 billion package."

Biden and Senate Majority Leader Chuck Schumer, D-N.Y., his party's lead bargainer, abandoned Biden's request to include $5 billion to help countries — especially poorer ones — where the disease is still running rampant.

The inability of Biden and top Democrats to protect the additional spending they wanted came after the two parties gridlocked over GOP demands to pay for it by pulling back unspent aid from earlier pandemic measures. It also reflected the diminished political force that battling COVID-19 has this election year, two years into a pandemic that began with bipartisan support for throwing trillions of dollars at it.

Sen. Mitt Romney of Utah, the lead GOP bargainer, hailed the accord as one that would address "urgent COVID needs." He also trumpeted the measure's savings, which he said meant it "will not cost the American people a single additional dollar."

Still uncertain was whether objections by some Republicans might prevent the Senate from considering the bill this week, as Biden and Schumer want, before Congress begins a two-week recess.

As their price for letting the bill move quickly, Republicans were considering demanding a vote on an amendment barring Biden from lifting immigration restrictions. At least 10 GOP votes will ultimately be needed for the legislation to get the 60 votes it will need to clear the 50-50 Senate.

"We have an agreement," Senate Minority Leader Mitch McConnell, R-Ky., said in a brief interview. "The question is when will we be able to process the bill, and honestly that's just not clear yet."

Some Republicans want an election-year vote on retaining curbs imposed by then-President Donald Trump during the height of the pandemic in 2020 that's let authorities immediately expel migrants crossing the border from Mexico for public health reasons.

The ban is due to end May 23. And while Democrats largely favor immigration, the lifting of the restrictions could cause political problems for moderates due to the massive increase in migrants that its lapse would prompt.

In the House, Speaker Nancy Pelosi, D-Calif., and many liberals have criticized the ejection of global assistance. But leaders signaled they were ready to accept compromise.

While short of Biden's agreement full request, "this package will fulfill immediate needs to secure more vaccines, boosters, testing and therapeutics to keep the pandemic at bay – and it must be enacted as quickly as possible," Pelosi set an a statement released overnight.

Schumer said members of both parties want to craft a second spending measure this spring that could include funds to battle COVID-19 and hunger overseas and more assistance for Ukraine as it continues battling the Russian invasion. The fate of such a measure is uncertain.

Romney also suggested an openness to considering future money. "While this agreement does not include funding for the U.S. global vaccination program, I am willing to explore a fiscally responsible solution to support global efforts in the weeks ahead," he said.

The agreement comes with BA.2, the new omicron variant, expected to spark a fresh increase in U.S. cases. Around 980,000 Americans and over 6 million people worldwide have died from COVID-19.

At least half the agreement's $10 billion would be used to research and produce therapeutics to treat the disease, according to fact sheets from Schumer and Romney.

The money would also be used to buy vaccines and tests. At least $750 million would be used to research new COVID-19 variants and to expand vaccine production, the descriptions said.

Administration officials have said the government has run out of money to finance COVID-19 testing and treatments for people without insurance. They've also said funds are running low for boosters, vaccines focused on specific variants, free monoclonal antibody treatments and care for people with immune system weaknesses.

The deal is also a reduction from a $15 billion version that both parties' leaders negotiated last month. Pelosi abandoned that plan after Democratic lawmakers rejected proposed cuts in state pandemic aid to help pay for the package.

The measure is fully paid for by pulling back unspent funds from previous pandemic relief bills that have been enacted, bargainers said.

Fact sheets said that includes savings from funds protecting aviation manufacturing jobs, assisting entertainment venues shuttered by the pandemic, helping states extend credit to small businesses and aiding agriculture.