Senate Republicans who have been maneuvering for weeks to get a new round of votes on legislation that would expand offshore drilling appear close to getting their wish.

Senate Majority Leader Harry Reid , D-Nev., appeared to surprise his Republican counterpart Monday by offering on the floor to allow each party to offer four energy-related amendments to a Democratic bill (S 3268) aimed at boosting regulation of speculation in the oil markets.

“It sounds to me like we’re very close to having a consent agreement,” said Senate Minority Leader Mitch McConnell , R-Ky.

Republicans in both chambers have complicated the agenda for Democrats on a broad range of legislation by pressing for votes on drilling amendments. The Senate has cast votes on a pro-drilling amendment and other GOP energy measures as recently as May, but Democrats have become increasingly uncomfortable with the idea of additional votes on pro-drilling measures. Substantial defections among their ranks could prove an embarrassment, strike a blow against the party’s pro-environment base and embolden the GOP.

But Reid’s offer indicates he might be ready to have that fight — and perhaps put it behind him for the rest of the year. “I think we’re getting very close to being able to reach an agreement to go forward,” McConnell said. “This is a significant step in the direction that I had hoped we might take.”

McConnell and other Senate Republicans huddled Monday night to discuss Reid’s offer. Afterwards, McConnell said he needs to consult with other members of the Republican leadership before accepting the offer, but he added that he should be able to get back to Reid soon.

“I’m very encouraged by this development,” McConnell said.

And John Cornyn of Texas, vice chairman of the Senate Republican Conference called the offer “a positive step” but said, “We’d still want to see more production.”

Reid said he would allow Republicans to offer amendments on expanding offshore drilling, exploration of oil shale resources, nuclear energy, and a larger energy package identical or similar to a GOP leadership energy proposal introduced in May (S 2958), also aimed at opening up new areas for drilling.

Reid said Democrats would also offer four energy-related amendments, but he did not specify what they would be.

The topic is expected to be discussed during the Senate Republicans’ regular Tuesday caucus lunch.

Under Reid’s offer, all of the amendments would require 60 votes for adoption — making it unlikely that any of the GOP amendments would be adopted. Still, the votes likely would draw some Democratic support and allow Republicans to claim there is bipartisan support for efforts to produce more domestic energy.

For Senate Democrats, the votes could mean the end, at least temporarily, of Republican tactics that have impeded action on a number of fronts.