LOUISVILLE, Ky.—Republicans took the Senate majority in a commanding sweep on Tuesday, winning nearly every contested race across the country, gaining governor's mansions and adding to their majority in the House of Representatives. For weeks, pundits had debated the semantics of what would constitute a "wave" election, but when it came, it was unmistakable.

Republicans unseated Democratic incumbents in Senate races in Arkansas, North Carolina, and Colorado, and were leading in Alaska early Wednesday. They easily held onto GOP-controlled seats in Georgia, Kansas, and Kentucky. In New Hampshire, Democrat Jeanne Shaheen barely held on against Republican Scott Brown. In one of the night's biggest surprises, Virginia Senator Mark Warner, who was thought to be safe, was up only half a point over his Republican challenger early Wednesday. The Louisiana election, in which Democrat Mary Landrieu finished slightly ahead of her Republican challenger, Bill Cassidy, was set to go to a December runoff, which Cassidy is favored to win.

Though Pennsylvania's abysmally unpopular Republican governor, Tom Corbett, was defeated, Republicans took over governor's mansions in Arkansas, Illinois, Maryland, and Massachusetts, and were leading by a hair in Colorado. Controversial Republican incumbents Scott Walker (Wisconsin), Rick Snyder (Michigan), Sam Brownback (Kansas), Paul LePage (Maine), Nathan Deal (Georgia), and Rick Scott (Florida), all of whom had appeared vulnerable in pre-election polls, all held on to win reelection.

Ebullient Republicans, many of whom had run relentlessly one-note campaigns focused on the unpopular president, touted the results as a rejection of President Obama and Democratic policies. "This race wasn't about me or my opponent," Mitch McConnell, the Kentucky senator who easily won reelection and stands to become the new majority leader, told a ballroom full of supporters here. "It was about a government people no longer trust."

Much speculation now focuses on McConnell, who has been blamed for singlehandedly stopping most of the Obama agenda for the past five years. (Ironically, the conservatives who want the Obama agenda stopped give McConnell little credit for doing so.) But McConnell now faces a choice about whether continued obstruction will serve his party's interests. In his victory speech, he mentioned no specific policies but rather struck a conciliatory note.

"Some things don't change after tonight," he said. "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, and he knows I won't either. But look, we do have an obligation to work together on issues where we can agree. Just because we have a two-party system doesn't mean we have to be in perpetual conflict."

The new Senate majority will mean the ascension of McConnell, a master politician who does not excel at the more public parts of the job—much like the outgoing majority leader, Harry Reid of Nevada. And it means the fall of Reid, who has led the majority since 2007, keeping a diverse caucus remarkably unified while changing the Senate rules and, Republicans complain, preventing most bills and amendments from being considered.

McConnell will now have his own fractious caucus to corral, starting with the junior senator in his own state, Rand Paul, who spoke from the same stage Tuesday night. Paul spoke of a sharply conservative agenda for the new Senate: tax cuts, balancing the budget, approving the Keystone XL pipeline, and "repealing every last vestige of Obamacare." McConnell will face pressure from conservatives like Paul and Ted Cruz of Texas to pursue a maximally confrontational approach—as Paul put it, sending Obama "bill after bill" and daring him to veto them all. On the other hand, Senate GOP pragmatists—likely including those just elected from blue states and those who face reelection in 2016—want the new majority to seek constructive compromise in order to prove to voters that Republicans can govern.

In an interview on Sunday, McConnell said his priorities would be "getting people back to work," principally by "pushing back against this overregulation," an allusion to the Environmental Protection Agency. But he also cited areas of potential agreement with Obama, beginning with comprehensive tax reform and free-trade agreements. On immigration, he said, "It's a possibility."

"I'm not opposed to doing business with the president," McConnell said. "He's going to be there two more years. If we can find ways to make some progress for the country, we ought to do it."

McConnell's counterpart in the House, Speaker John Boehner, also finds his hand strengthened by Tuesday's results, having added at least 10 seats to his Republican majority. Once beset by rumors he would retire or be dethroned, Boehner now faces no known challenger for the speaker's gavel. On the one hand, a larger majority will give Boehner more room to maneuver—he will be able to pass bills while losing more Republican votes. But on the other hand, many of his new members will be conservatives from deep-red districts, who may be disinclined to go along with any bipartisan compromises proffered by the Senate.

Why did Democrats lose? Exit polls pointed to an electorate that strongly resembled that of 2010, when the older, whiter electorate that favors Republicans turned out enthusiastically, while the young, non-white electorate that favors Democrats largely stayed home. The working-class vote—defined as voters making less than $50,000 per year, a crucial demographic for Democrats—was only 37 percent of the electorate, comparable to 2010, when it was 36 percent. Those voters favored Democrats by a 14-point margin; the party generally wins when the margin approaches 20 points. Look for many Democrats to argue that the party must put more emphasis going forward on a populist economic message.

Plenty of other factors conspired against Democrats. Obama's popularity has dropped steadily for the last year as he faces crisis after crisis—some impossible to anticipate and some of his own making, from the rollout of Healthcare.gov (though, liberals note, opposition to Obamacare was not a major theme of many Republican campaigns) to the Islamic State insurgency, the border crisis, and the Ebola epidemic. Democrats' expensive, much-touted effort to expand the midterm electorate through field organizing in targeted states proved unavailing—indeed, it was Republicans, not Democrats, who surprised the pundits by doing better than polls had forecasted across the map. Late Tuesday, Democratic recriminations had already begun to fly, with Reid's staff openly blaming the White House for Senate Democrats' losses in The Washington Post.

But Republicans also earned their win by capitalizing on their opportunities, rather than squandering them as they've often done in recent years. The GOP establishment rallied early to beat back Tea Party primary challengers, spending tens of millions of dollars but largely succeeding. No Senate incumbent lost a primary, and open-seat contenders viewed as fringe candidates were defeated or pushed out of contention across the board. The only high-profile primary defeat was the shocking June loss of House Majority Leader Eric Cantor. In the place of past years' memorably batty GOP nominees, from Sharron Angle in 2010 to Todd Akin in 2012, was a polished, palatable class of Republicans whom voters could envision representing them in Washington.

The new Republican senators are quite conservative, perhaps more so than any previous class, but they are capable of sounding reasonable and staying focused on issues voters care about. The question yet to be answered is one of tactics: When these new players come to Washington, will they seek pragmatic accommodation? Or will they team up with the likes of Cruz, putting new faces on the same old gridlock?