WASHINGTON – The past four years of intense partisanship would suggest that a Republican seizure of the Senate Tuesday night will lead to two years of hopeless gridlock.

But instead of deepening the paralysis, the GOP’s win may alleviate it. Lost in the recent politicking is the fact that President Barack Obama and congressional Republicans may be able to find common ground on some serious, substantive goals. Overhauling Medicare and Social Security, rewriting the corporate and individual tax codes, passing some kind of immigration reform – these issues have bipartisan support, and both sides have signaled they would be willing to compromise.

With wins in Iowa, Colorado, West Virginia, Montana, North Carolina and Arkansas, Republicans secured enough to seats to win control of the Senate. Taking most of the closely contested races, Republicans won a resounding victory Tuesday night to secure control of the Senate. 

Even before all the votes had been counted on Tuesday, President Obama invited a bipartisan group to meet with him on Wednesday, obviously trying to get the new era off to a cordial start. And Republican Sen. Mitch McConnell of Kentucky, now the likely Senate Majority Leader, was already previewing the possibility of compromise. 

“Some things don’t change after tonight,” he said in his victory speech. “I don’t expect the president to wake up tomorrow and view the world any differently than he did when he woke up this morning. He knows I won’t either. But look, we do have an obligation to work together on issues where we can agree. I think we have a duty to do that. Just because we have a two party system doesn't mean we have to be in perpetual conflict.”

Senator Harry Reid, the now-former Senate Majority Leader, said he congratulated Senator McConnell. "The message from voters is clear: They want us to work together."

Both parties have a stake in Washington’s success. Obama has two years left to define his legacy. On immigration and environmental regulations -- and many foreign policy decisions -- the president can go it alone. The White House is insistent that Obama can use executive orders to accomplish many of his goals. But to succeed on the big items, he needs to work with Congress.

The Republicans, in control of the House for the past four years, earned their reputation as the “Party of No.” Looking ahead to 2016, though, they are beginning to recalibrate their tactics. Continued naysaying -- like pushing the budget process to another government shutdown, for example -- risks hardening the perception that they can only obstruct, not lead, or that they are hostages of the far right.

“If they get the Senate, they’d better do something,” former Democrat Pennsylvania Governor Ed Rendell said Sunday in an appearance on CNN’s State of the Union. “They’d better send the president some responsible pieces of legislation, or they’ll get crushed in 2016.”

Congress must pass some kind of spending bill before the new year, whether a short-term continuing resolution or a comprehensive “omnibus bill” that would fund the government through September 2015. Next year, the negotiations over the budget could lead to the kind of “grand bargain” that has eluded Congress in the past, one that would deal with Medicare, Social Security and taxes.

There are philosophical divisions. Democrats adamantly oppose raising the retirement age. Republicans support changing the tax code, but only in a way that doesn’t result in more tax dollars. But the desire to avoid another fiscal crisis will offer an incentive to try to hammer out some of the differences.

"Reagan and Tip O'Neill found things that they could agree on. Bill Clinton and Newt Gingrich found things that they could agree on. My first choice is to make some progress for the country," McConnell said in a CBS interview over the weekend. "And the only way to do that with the president in the office is with his involvement. So that's my first choice."

Before he wrestles with Obama, though, McConnell will have to wrangle his own party. Despite some superficial peacemaking during the general election, when many tea partiers chose to back moderate Republicans rather than cede control to Democrats, the GOP is still riven by infighting. Conservatives shut down McConnell’s campaign phones when he suggested he might not be able to hold a vote in the Senate to fully repeal the Affordable Care Act, a position his campaign later walked back. Many conservatives will be looking to demonstrate their power: Attaching a full repeal of ACA, also known as "Obamacare," to a spending bill that would keep the government open, launching another round of investigations into the IRS or Benghazi.

Repealing Obamacare remains the holy grail for the hard right. And with control of both chambers, Republicans will have an easier time bringing a bill to the floor for votes and sending a repeal to the president. Obama will veto it, of course -- which might in fact be in the Republicans’ best interest. Polls show that while the public dislikes “Obamacare,” many pieces of the act -- letting young people stay on their parents’ insurance, mandated preventive care, the elimination of lifetime caps -- are popular. Millions of people across the country are now insured through the exchanges, many of them receiving tax credits to help them defray the cost. Taking away that coverage would be political suicide for the GOP.

Dismantling pieces of the health care law is more likely to be a winning strategy for Republicans, even if it won’t satisfy the right. There is bipartisan opposition to the medical device tax, for example.

Obama could also do the Republicans a favor by using executive orders to reform U.S. immigration law. He held off until after the election in order not to give opponents another issue to run on. Now he can take take several steps, including delaying deportations of those who are already in the country illegally and continuing rules that allow the children of immigrants, known as Dreamers, to remain in the country.  And some Republicans are open to that approach, hoping to quiet the loud opposition within their party so they don’t alienate Latino voters before the 2016 campaign. In response to the Democratic push for immigration reform, Republicans will demand tighter border security. It’s likely they can move such legislation through both chambers.

On budget issues, Republicans have been unafraid to go to the brink, and beyond. Last year, disputes between Obama and congressional Republicans resulted in a 16-day government shutdown.

Republicans have called on Democrats to decide how federal dollars are spent by writing a budget and then using that budget to pass spending bills. The practice is known as “regular order” and has largely been ignored for the duration of Democratic control. Now the Republicans may be able to force that process. A genuine budget process may allow compromise, Republicans giving some room to increase spending and Democrats signing off on changes to large programs like Medicare and Social Security. It would be a messy procedure and make nobody completely happy. But it would still be a negotiation, worked out in a relatively sane manner -- not a manufactured crisis.

Obama has shown himself willing to give Republicans a little of what they want, like changing the way cost of living payments are adjusted for inflation. But he faced strong opposition from his own party. Now the White House needn't worry as much about offending progressives.

With the loss of the Senate, some Democratic dreams are gone. It’s hard to imagine that bills on gun control, carbon emissions or equal pay will make it to a vote. But none of those was likely to move forward with anything less than Democratic control of both houses, in any case.

Presidents have their greatest autonomy in dealing with foreign policy and it's not unusual for a lame duck president to become increasingly involved with foreign affairs. While some conservatives are likely to bristle at any moves Obama makes, he will still be able to avoid time-consuming fights on the floors of both chambers.

Meanwhile, both sides know what to expect from leadership; their relationships are pretty well established. It is near certain that McConnell will become Majority Leader and that Sen. John Cornyn, R-Texas, will remain the whip. Despite progressives’ distrust, Harry Reid is likely to assume the title of minority leader. Sen. Ted Cruz, R-Texas, looks set to continue his role as right-wing point man. 

In the House, Speaker John Boehner, R-Ill., survived a conservative revolt two years ago and will probably hang on. When Majority Leader Eric Cantor lost his primary bid and stepped down, Rep. Kevin McCarthy, R-Calif., took over as leader. Rep. Steve Scalise, R-La., then took on the role of whip (a move that was meant to appease conservatives but did little to calm their frustration with party leadership). Minority Leader Nancy Pelosi, D-Calif., will probably also stay in her role. She was successful in keeping Democrats mostly in lockstep during the shutdown last year and has been described as the most successful whip in Congress.

A fresh start at the top might have been welcome, but it also might have meant a rocky getting-to-know-you period with grandstanding by newbies determined to make names for themselves. 

This was the most expensive midterm election in U.S. history. If it, oddly, has the effect of ending gridlock, American voters may come to believe the money was well spent.