(CNN) Utah GOP Sen. Mitt Romney said Thursday that Republicans have struck an "agreement in principle" with Democrats on a $10 billion package to help US efforts to combat the Covid-19 pandemic, a breakthrough that could pave the way for new funds to help the United States' response efforts amid growing fears that critical resources are being depleted.
Romney, the lead GOP negotiator, told reporters the plan is "entirely balanced by offsets." He said the bill text still needs to be drafted and there needs to be a cost estimate from the non-partisan Congressional Budget Office before the Senate can vote on the matter.
The Senate, as a result, is expected to scrap Thursday afternoon's procedural vote on the issue -- in order to give time for the bill's text to be drafted and for an official CBO score.
In remarks from the Senate floor, Majority Leader Chuck Schumer said negotiators are "close to a final agreement that would garner bipartisan" support.
"We are working diligently to finalize language of scoring and the final agreement on what should be funded in the final COVID package both domestic and international," Schumer said. "As a sign of good faith, and to encourage us to come to a final agreement, I will reschedule today's procedural vote to a later time."
The goal is to pass the bill next week, Romney said.
The $10 billion price tag overall is less than half of what the White House was seeking. It's also less than the $15.6 billion that had been included in the government funding bill earlier this month, but had to be scrapped after a number of House Democrats opposed the way the money had been offset.
Sen. John Thune of South Dakota, a member of GOP leadership, expressed skepticism that the package could be finished by next week.
"If there was a deal we would be voting on it ... People want to see scores and top lines and what's in it," Thune said.
Democrats also urged caution regarding progress of the talks. Senate Majority Whip Dick Durbin pushed back on Senate Republicans saying that there is a "deal in principle."
"I can't go that far," he told reporters. "Schumer's just said he's still working on it."
Romney said the bill would be paid for "almost exclusively" by redirecting money from the American Rescue Plan -- the law that Democrats pushed through last year. As part of the offsets, he said that they are pulling money that would have gone to states to provide grants for local businesses.
Sen. Roy Blunt, a Republican from Missouri, told reporters additional offsets would include taking money from a fund that had been intended to go to shuttered concert venues and theaters during the pandemic. He estimated there was still about $2.2 billion from that account Democrats and Republicans could re-purpose. He also said there was aviation manufacturing money from past legislation that totaled around $2 billion that could also be used.
The money is expected to go half toward therapeutics, Blunt said. He added the secretary of the Department of Health and Human Services would then have "a lot of discretion" on how to best use the other half of the funding.
Romney said there "may be $1 billion" of money to deal with global Covid response efforts, even as Democrats were pushing for $5 billion in global aid.
Romney and Blunt predicted there would be "a lot more than 10" Republicans who would back it.
"I believe we get more than 10 Republicans maybe even significantly more," Blunt said.
The announcement comes after President Joe Biden made a desperate appeal Wednesday for Congress to pass additional funding and fast.
"Congress has to provide the funding America needs to continue to fight Covid-19. We're already seeing the consequences of congressional inaction," Biden said Wednesday, adding that the administration already did not have money to purchase monoclonal antibody therapies, vaccines, and more tests.
The White House has spent weeks warning lawmakers that if Congress didn't act soon they would expire money for vaccinations, to reimburse providers and insurers for out-of-network treatment, underwrite Covid testing and supply personal protective equipment.
"Congress, we need to secure additional supply now, now. We can't wait until we find ourselves in the midst of another surge to act. It will be too late. And we also need this funding to continue our efforts to vaccinate the world," Biden said.
Asked about the tentative deal Thursday, Senate Minority Leader Mitch McConnell would only say: "We're working on it, we will get there."
This story has been updated with additional developments Thursday.