Can Republicans fix Congress? It could be up to these Democrats.

Democrats may now be in the minority in the Senate, but a clutch of their centrists will hold particular sway as bridge-builders – and powerbrokers.

In order to get anything done, the Republican majority of 54 still needs six Democrats – more if some GOP members peel off – to clear procedural hurdles and bring legislation to a vote.

And Republicans will be under substantial pressure to get things done in the next two years. To give themselves the best chance to hold the Senate and win the White House, Republicans will have to show that they can govern effectively, the thinking goes. And to do that, they will need at least a handful of Democrats in the Senate.

"Democratic senators from purple and red states will play a decisive role” in consensus-building, writes former Sen. Olympia Snowe, a key Republican bridge-builder herself during her years in Congress, in an e-mail.

In interviews, potential aisle-crossing Democrats expressed willingness to work with the new Republican majority, led by Sen. Mitch McConnell of Kentucky. But don’t expect them to be pushovers. They have their own issues and interests to watch out for. They also can’t be considered as a voting bloc, because their votes will depend on the issue.

Still, several say they want to help break the gridlock that has come to characterize Congress.

“If there was one message I heard from a much closer election than I or others anticipated, it was that people want us to get stuff done,” said Sen. Mark Warner (D) of Virginia, in the waning days of the 113th Congress – the second least-productive Congress in modern history.

Senator Warner is on the Republicans’ “go-to” list of Democrats, along with Sens. Tim Kaine (also of Virginia), Joe Manchin of West Virginia, Heidi Heitkamp of North Dakota, and Joe Donnelly of Indiana. Independent Sen. Angus King of Maine, who caucuses with the Democrats, is also a top prospect for Republicans. 

The dealmaking is moving quickly.

On Wednesday, Senator Donnelly joined Sen. Susan Collins (R) of Maine to unveil proposed changes to the Affordable Care Act. The legislation would change the ACA definition of full-time employment from 30 hours per week to 40 in order to prevent companies from reducing employees' hours to avoid the employer mandate. The House is expected to pass a similar measure this week.

On Thursday, the Senate energy committee is expected to hold a hearing on legislation to approve the Keystone pipeline – the Senate’s first order of business. The legislation includes six Democratic cosponsors. Again, the House is expected to pass Keystone this week.

In both cases, however, it's unlikely that Senate Republicans can muster enough Democratic support to overcome a promised presidential veto – 67 votes would be needed.

Going forward, other red-state Democratic senators could come into play, such as Claire McCaskill of Missouri and Jon Tester of Montana. But Senator Tester may be a tougher “get” for the GOP.  Like Senator McCaskill, he is a Keystone cosponsor and has bucked his party before. But he is also the new chairman of the Democratic Senatorial Campaign Committee charged with putting more Democrats in the Senate in 2016. 

When asked whether he sees a group of Democrats as potential bridge-builders, Tester answers without hesitation, “I do.” He adds: “I’m looking for ways to make things work better, to improve stuff, whether it’s Dodd-Frank [financial regulation] or the Affordable Care Act.”

But, he cautions, “those bills are in place for a reason, and as long as we’re improving them – and not destroying them – there’s a lot of common ground that we can move forward on.”

McCaskill says that whether Democrats join with Senator McConnell will depend largely on Senator McConnell: “If he tries to push a bill that is 90 percent moderate and progress on a problem, but then he puts 10 percent of it in there that is a deal-breaker, so to speak, I don’t think any of us are interested in being manipulated.”

Meanwhile, these Democrats would like McConnell to help them, too.

For Warner, it’s finding alternatives to the across-the-board mandatory spending cuts known as “sequestration,” which is battering defense contractors in northern Virginia, as well as ways to increase spending on infrastructure. For McCaskill, it’s passing a bill addressing sexual assault on college campuses that has bipartisan support. For Tester, it’s forest management legislation.

The need for Republicans to shed their "party of no" label could give these Democrats a powerful bargaining chip.

Indeed, Election 2016 is shaping up to be a daunting one for Republicans. For one, they have 24 senators up for reelection, while Democrats have only 10. That's more than twice as many seats to defend. Moreover, seven of those seats are in states that President Obama won twice.

In addition, 2016 is a presidential election year, which usually brings out a more diverse – and Democratic-leaning – electorate. That means Republicans will need to do better among more-moderate voters both to retake the White House and to keep control of the Senate.

Just as moderate Republicans influenced legislation when Democrats controlled the Senate, so, too, will moderate Democrats “extract a price” for dealmaking in the GOP-controlled Senate, says Robert Browning of Purdue University in Indiana.

“The math is inescapable,” says McCaskill. McConnell “has 54 votes and he needs 60.”