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In Kansas recently, Republican Senator Pat Roberts, who’s in a tough race for reelection, made a statement that left me puzzled. “A vote for me is a vote to change the Senate back to a Republican majority, and we’ll get things done,” he said. “And it means a stop to the Obama agenda.”

Wait a minute, I thought. Which is it—ending the status quo of Washington gridlock? Or ratcheting up the gridlock by obstructing President Obama? You can't "get things done" in Washington without the president's signature, and no matter what happens in this year's elections, he's not going anywhere for another two years.

Yet these two seemingly contradictory messages are at the heart of Republican Senate campaigns across the country. I’ve heard them from candidate after candidate. And the paradox behind them gets to the question political watchers are increasingly pondering: If, as seems likely, Republicans take the Senate, what then? Will the GOP see its takeover as a mandate for ever more extreme partisanship? Or will the party suddenly turn conciliatory, ushering in a new age of progress? A new Republican Senate majority will put the party at a crossroads as it tries to reconcile these two competing promises.

One possibility is that nothing will really change. After all, we have divided government now, and we will still have divided government if Republicans go from 45 senators to 51. Obama will still be in the White House, and the House of Representatives will still belong to the GOP. With the Senate requiring a 60-vote supermajority for most legislation, Republicans have effectively had a veto in the upper house since Scott Brown was elected in 2010. Democratic priorities like gun control or a minimum-wage hike wouldn't be any deader in a Republican-controlled Congress than they already are. The status quo is often a good bet in Washington, and it may well be that it simply continues.

A Republican Senate majority would still change a few things, however. It would make it harder for Obama to get his nominees approved, something Democrats have been able to do with just 51 votes since they changed the Senate rules with the “nuclear option” last year. It would make Mitch McConnell the majority leader, with the power to decide what legislation gets considered and how it proceeds through the legislative process. Given McConnell’s track record of keeping Republicans staunchly unified against virtually anything Obama proposes, many observers, particularly liberal pundits, believe McConnell would quickly devote the Senate to passing a raft of partisan legislation that Obama would never allow to become law: repealing Obamacare, defunding Planned Parenthood, approving the entitlement-slashing House budget plan authored by Representative Paul Ryan, restricting the Environmental Protection Agency, and so on. The result would be a more partisan, toxic, and stalemated Washington than ever before.

There’s evidence to support this view. In an interview with Politico in August, McConnell said he planned to “challenge” Obama by passing spending bills that included “a lot of restrictions on the activities of the bureaucracy.” That is, Republicans would attach their policy priorities—McConnell specifically mentioned reining in the EPA—to the legislation that funds the government, forcing Obama either to approve their pet projects or shut down the government. On the trail, GOP candidates like Roberts frequently make reference to the bills the House has passed that the Senate hasn’t taken up. There are 387 of them—you can find a full list here—ranging from the “Permanent Electronic Duck Stamp Act of 2013” to bills that would expand offshore oil drilling and get rid of all or part of the Affordable Care Act. Many are what’s known as “messaging bills”—legislation that House Republicans knew would never become law and passed just to make a statement about their priorities, or to satisfy a constituency. Sending those bills through the Senate would result in a speedy Obama veto, accomplishing nothing.

But those who see McConnell only as an obstructionist are overlooking another significant part of his profile: his record as a dealmaker. As the general election nears, McConnell has sought to emphasize this as well. “There have been three major bipartisan agreements during the Obama years between Republicans and Democrats,” he said in last week’s Kentucky Senate debate with his Democratic opponent, Alison Lundergan Grimes. “The vice president and I have negotiated every one of them.” McConnell was referring to the December 2010 deal to extend the Bush tax cuts, the last-minute 2011 deal to raise the debt ceiling, and last year's fiscal-cliff deal. This is the side of McConnell that drives conservatives crazy, putting him in the unique position of being ardently reviled by left and right alike. But as Alec MacGillis’s excellent new ebook on McConnell makes clear, the Kentucky senator’s top priority has always been not ideology but his own political advancement and survival. He made those deals because, much as his base hated to see him working with Democrats, the alternative would have been even worse for the GOP—and him—politically.

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.