The new agreement would save $50 billion by delaying a Medicare rebate rule passed under President Donald J. Trump and raise nearly $30 billion by applying tax information reporting requirements to cryptocurrency. It also proposes to recoup $50 billion in fraudulently paid unemployment benefits during the pandemic.

Republicans blocked the Senate from moving ahead with the plan last week, saying that too many issues remained unresolved. Mr. Portman’s comments and those of other Republicans in the group, who spoke after meeting with Senator Mitch McConnell of Kentucky, the minority leader, suggested that they would now allow it to move forward.

It remained unclear whether enough Republicans would join the five core negotiators in advancing the measure, although a handful of G.O.P. senators outside the group signaled that they would be open to doing so.

“It’s not perfect but it’s, I think, in a good place,” said Senator Thom Tillis, Republican of North Carolina, who said he would vote in favor of taking it up.

Some Senate Democrats, including at least one key committee chairman, said they were still reviewing the plan before deciding whether to support it.

But Senator Chuck Schumer, Democrat of New York, said he believed “we have the votes.”

If they do, Democrats would still have to maneuver the bill through the evenly divided Senate over a Republican filibuster, which will require the support of all 50 Democrats and independents and at least 10 Republicans. That could take at least a week, particularly if Republicans opposed to it opt to slow the process. Should the measure clear the Senate, it will also have to pass the House, where some liberal Democrats have balked at the emerging details.

The five Republicans who have spearheaded the deal with Democrats — Mr. Portman and Senators Susan Collins of Maine, Lisa Murkowski of Alaska, Bill Cassidy of Louisiana and Mitt Romney of Utah — urged their colleagues to support a measure they said would provide badly needed funding for infrastructure projects across the country.