WASHINGTON (CNN) -- Senate Majority Leader Harry Reid surprised Republicans on Monday by offering them a chance to vote this week on four GOP-backed amendments to an energy bill, including one that would expand offshore oil drilling.
Senate Majority Leader Harry Reid says Democrats would offer four of their own proposals, too.
The Senate has been gridlocked for days on the bill -- which would attempt to curb speculation in the oil futures market -- as both parties argued over which amendments will be put to a vote.
Senate Minority Leader Mitch McConnell, R-Kentucky, said he was "very encouraged" by Reid's proposal, but McConnell added he would have to confer with his leadership team.
The possible breakthrough comes days before Congress recesses for August and lawmakers return home to face constituents anxious for relief at fuel pumps.
GOP leaders met late Monday and were expected to discuss the plan with the full Republican membership Tuesday. But two leadership aides said Republicans probably would seek more than four amendments.
Republicans had been insisting they should be allowed to offer two dozen or more amendments. Watch how energy has turned into an election issue »
"It has to be north of four," one of the Republican aides said. Another added, "I mean, come on, that's not negotiating."
But a Democratic leadership aide predicted Republicans "won't take yes for an answer." And Sen. Charles Schumer, the Senate's third-ranking Democrat, said Democrats believe Republicans "will say nothing is ever enough."
"These are there four major amendments," Schumer said. "We'd love to have a deal, but I thought Harry's offer was a very generous offer."
Reid, D-Nevada, said Democrats would allow votes on GOP amendments that would permit new drilling on the outer continental shelf; the development of oil shale in Western states; construction of new nuclear power plants; and broader legislation that Republicans have dubbed "find more, use less." See how gas prices have risen across the country »
That legislation includes expanded offshore drilling, conservation initiatives, the improvement of battery technology, and language to curb speculation in the oil futures market. See how speculation has increased oil prices »
Democratic leaders have generally opposed efforts to repeal a 1981 law barring most offshore drilling.
Reid said Democrats would offer four of their own proposals, but didn't specify what those would be. He said all amendments would need 60 votes to pass, a threshold that could make it difficult for any of them to succeed.
Republicans, buoyed by recent polls showing a majority of Americans support new offshore drilling, have said they are confident they can get more than 50 senators to support expanded drilling, if not the 60 votes needed to pass.
Energy legislation also has been stalled in the House.
A bipartisan "energy working group" of 28 lawmakers hopes to break the impasse this week by proposing a compromise that couples new offshore drilling with conservation and renewable energy programs.
Yet House Speaker Nancy Pelosi, a California Democrat, says she won't allow a vote on a bill that includes new offshore oil drilling.
Also this week, the House is expected to vote on its version of an antispeculation bill. Republican leaders have not decided if they will support the bill.
CNN's Deirdre Walsh contributed to this report