The narrative of the GOP’s outsize rout is fast drying in cement. So the question turns to the newly-empowered party’s mandate: Do they have one? If so, for what?

The GOP establishment brains responsible for engineering the party’s gains already are urging humility. Their mantra today: “This is not a mandate, it’s an opportunity.” Congressional Republican leadership hewed to the message as the scale of their victory became clear last night. House Speaker John Boehner, in a statement, said Republicans are “humbled by the responsibility” and will skip celebrating in favor of getting to work. Senate Republican leader Mitch McConnell, who romped over his own challenge back home in Kentucky from a young, energetic Democrat, struck a peacemaking note in his victory speech: “We do have an obligation to work together on issues where we agree,” he said. “Just because we have a two-party system doesn’t mean we have to be in perpetual conflict.”

That might sound bizarre from a figure widely understood to be the architect of Republicans’ programmatic opposition to Obama. But the numbers behind the GOP gains tell part of the story: Voter interest in the election was the lowest of the last six midterms; those who did show up registered equally dismal feelings about Obama and Republican leaders, with nearly 6 in 10 describing themselves as dissatisfied or angry with both; and broadly, Republicans actually rated below Democrats in voter approval, with 40% reporting a positive view of the GOP, compared to 44% for the president’s party.

The numbers on Capitol Hill tell the rest of the tale. Yes, Boehner expanded his grip on the House to at least 242 seats, on track to piling up the largest Republican majority in that chamber since the Truman administration — a margin that should make Boehner’s job easier. But the real action for the next two years was always going to be in the Senate, where the 60-vote threshold for accomplishing most of anything will force McConnell to go hunting for Democratic votes. He’ll need even more — 67 — to overcome a veto pen Obama has so far only wielded twice in his presidency but will likely use more frequently in the remainder of his second term. Given those hurdles, the difference between a 51-seat majority and a 53 or 54-seat one seems almost academic.

And so the duty for Republicans becomes two-fold: Managing expectations about what they’re able to get done given the real checks that remain on their power, and then actually delivering some accomplishments to show they’re equal to the responsibility of governing. The strategists and moneymen who coauthored the Republican victory are already working to communicate that message to the victors.

“It’s first and foremost a rebuke to President Obama and his policies, but it’s also a reality check and a second chance for Republicans,” says Steven Law, a former McConnell aide now running American Crossroads, the Karl Rove-affiliated super PAC that spent nearly $22 million helping elect Republicans. And Law, notably, is counseling caution. “Republicans need to keep in mind this election wasn’t primarily about them… The voters are going to expect Republicans to put good, practical solutions on the president’s desk.”

That means no more debt-ceiling brinkmanship when the country faces the next deadline to lift its borrowing authority in March. And, relatedly, no more pressing a dead-end bid for a wholesale repeal of Obama’s health care law. On the contrary, there is a list of business-friendly, smaller-bore agenda items Republicans can dust off in hopes of striking compromises with the White House — on trade deals, energy projects, and patent reform. Sen. Ted Cruz (R-Texas), captain of last year’s disastrous government shutdown gambit, missed or ignored that memo in the run up to Election Day, insisting he’d press his party to double down on confrontation. By Tuesday night, he looked like a churlish caucus of one when he appeared on CNN and refused to say whether he’d support McConnell’s ascension to majority leader (just moments after the current titleholder, Nevada Democrat Harry Reid, placed a call to McConnell, conceding).

But if Cruz is dealing himself out of the work of governing, it only highlights McConnell’s burden. After all, the Kentucky Republican now stands poised to realize his career ambition of leading the Senate after flawlessly executing a long game built on denying Obama any Republican cooperation. The strategy both stoked and was reinforced by the Tea Party uprising on the right — a movement that ended up turning on the party, complicating McConnell’s project of capturing Senate control. This year, McConnell’s path to victory required him to stamp out the last of the rebellion’s brushfires and then train the focus back on the President. In both cases, it meant defining Republicans according to what they aren’t. The work of finally filling in those blanks awaits, and it will not be easy.