WASHINGTON — In the past few days, a bipartisan group of 12 senators has come together to push both parties toward a compromise, hoping to reopen the government and raise the national debt ceiling all at once.

These 12, led by Sen. Susan Collins, R-Maine, and Sen. Joe Manchin, D-W.Va., are not the Senate’s usual impact players.

Five of them are in their first term in office. Three of them are in their first year in office – in a chamber where, traditionally, time turns into power at roughly the speed that dead plants turn into oil.

But, after weeks of deadlock, this small group seems to have given party leaders a blueprint to end the crisis. What sets these 12 apart, analysts say, is that – in an era of powerful polarizations – these senators have personal or political reasons to seek an answer in the middle.

“Either they’re temperamentally . . . pragmatists and moderates. Or they come from states where they aren’t a perfect fit for the voters – where they need to demonstrate their political independence,” said Stuart Rothenberg, an independent political analyst who runs the Rothenberg Political Report. The result, Rothenberg said, is a drive to “work from the middle, for the middle.”

This loose group has been at the center of the shutdown crisis since Friday, when its members proposed an agreement that would have raised the debt ceiling until Jan. 31 and funded federal agencies through March.

Democratic leaders rejected that proposal over the weekend, because it would allow a new round of “sequester” cuts to take effect in January. But the proposal started a new round of intense negotiations, which continued Monday when the group met for two hours in the morning.

If a deal is struck – probably by Senate Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky. – these 12 could be crucial in selling it to their colleagues.

The best-known member of the group is probably Sen. John McCain, R-Ariz., the 2008 Republican presidential nominee famous for his “maverick” politics. On Monday, McCain said the group was working on the details of an agreement: “We’re on dates and times. We’re working on specifics,” he said. “We have outlines of what we think. We still have some differences.”

The rest of the group includes several senators who are independent by personality. Sen. Amy Klobuchar, D-Minn., was ranked the Senate’s 30th most liberal member in 2012, according to vote rankings compiled by the National Journal. But Klobuchar touted her work as a dealmaker in last year’s reelection campaign: In one speech, she was quoted saying, “I refuse to obey the fence lines . . . instead, I get things done.”

Collins, in office since 1997, is a Republican moderate who has frequently voted with Democrats – including on the 2009 stimulus bill. Sen. Angus King, I, Maine’s other senator, won his election as an independent last fall (though he caucuses with the Democrats).

Manchin has been in office only since 2010, but he has established himself as a would-be architect of compromise. During the gun-control debate that followed the school massacre in Newtown, Conn., Manchin struck a deal with Sen. Mark Kirk, R-Ill., and Sen. Patrick Toomey, R-Pa., that would have tightened some gun regulations.

That deal ultimately failed, but it established Manchin as an independent voice in the Senate. That persona fits Manchin’s political situation: He represents a state that is shifting quickly toward Republicans, so Manchin’s best hope might be to underscore that he is not a pawn of his own party.

Several others among the 12 find themselves in similar political situations. Their states have either swung between the two parties or, in some cases, turned solidly to the other side.

Three of the Republicans on the list – Kirk, Sen. Lisa Murkowski, R-Alaska, and Sen. Kelly Ayotte, R-N.H. – come from states whose other senator is a Democrat. Three of the Democrats – Sen. Mark Pryor, D-Ark., Sen. Heidi Heitkamp, D-N.D., and Sen. Joe Donnelly, D-Ind. – come from states whose other senator is a Republican.

For all of them, there is danger in appearing too close to their party’s extremes. Pryor might be the most endangered of the Democrats, facing reelection next year. His campaign website says he is working to find “common ground and bipartisan solutions.”

The 12th member of the group is Sen. Mike Johanns, R-Neb. Johanns is in his first term, but he has reached that special part of a senator’s career that allows for a flourishing of independent thinking.

“There’s no risk for him here. He can do what he needs to do,” said Jennifer Duffy of the nonpartisan Cook Political Report.

Which is to say: Johanns has announced that he’s not running for reelection.