When and if they take control of the Senate, Republicans will have a big incentive not to simply create more gridlock: It would make them look terrible, worsening their image as the “party of no” and making it harder for their presidential nominee to win in 2016. The same goes for passing unpopular legislation like the Ryan budget or repealing Obamacare—which most voters do not favor, even though the law is also unpopular. As things stand today, neither party is to blame when Congress can’t get anything done, because each party controls half of the Capitol. (While the House’s dysfunction is well known, the Senate has also become a legislative graveyard, to the point that even Democratic senators publicly complain about it.) But with control of both houses of Congress, Republicans would be on the hook for Congress’s actions. They alone would get the blame if Congress remained dysfunctional—and they alone could claim credit if Congress actually passed bills with popular support. If Republicans passed such moderate, constructive legislation, Obama would be hard pressed to simply veto everything they put on his desk.

“The way I describe it is, we’re putting the guardrails on the Obama administration’s last two years,” Senator Rob Portman told me in a recent interview, explaining how he envisions a Republican-controlled Senate proceeding. Needing GOP approval for nominees, Obama would have to appoint moderates to judicial and executive positions, he said. But Portman, a fiscally focused Ohio Republican who is generally conservative but believes in bipartisan compromise, sees several areas of potential cooperation with the administration. He mentioned tax reform, a “grand bargain” on the budget, an energy bill—perhaps something that combines Keystone XL pipeline approval with reductions in carbon emissions—and new free-trade agreements, which Obama has supported but Senate Majority Leader Harry Reid has blocked. Portman, who voted against the bipartisan immigration-reform bill that passed the Senate last year, also believes a Republican-led immigration-reform bill could pass the House and Senate and potentially be approved by Obama.