A day after McConnell, the incoming Senate Majority Leader, told reporters in Louisville, Kentucky that the midterm voters sent a message to the parties to work together, Boehner, the House Speaker, offered a more aggressive interpretation. “My job is to listen to the American people,” the Ohio Republican told reporters gathered Thursday in the Capitol for his first post-election press conference. “The American people have made it clear they’re not for Obamacare. Ask all those Democrats who lost their elections Tuesday night.”

Exit polls revealed a dour electorate, with 78 percent worried about the direction of the economy and 70 percent reporting their own financial situation is the same or worse than it was two years ago. It should be no surprise, then, that they ranked the economy their top concern, 20 points ahead of health care. On President Obama’s signature law itself, they were divided, with 46 percent saying it was about right or didn’t go far enough and 49 percent declaring it an overreach. Another election night poll found nearly six in ten voters said their vote was not intended to send a message about the law.

Then there’s the matter of who actually voted. One estimate is pegging turnout at 37 percent of eligible voters, the lowest participation rate since 1942. Not exactly a ringing endorsement for either side.

Distilling the will of a fragmented, partial electorate is tricky work and there may be no right answer. But there are certainly some wrong answers, and Boehner struck on one. He knows it. This is the same guy who declared the measure “the law of the land” in the days after the 2012 election. But he leads a Republican majority that owes its margin to lawmakers bent, Sisyphus-like, on continuing to push wholesale repeal, no matter the practical impossibility of achieving it as long as a Democrat sits in the Oval Office and the GOP lacks the numbers in Congress to override a veto.

And that’s what’s really going on here: McConnell and Boehner are each doing a balancing act. The divergent natures of their chambers dictate different approaches to the same problem. In the House, where a bare majority rules, Boehner’s firmer grip on his gavel will license a more strident tack — and the continued strength of his right flank will demand it. McConnell will still need to peel off a handful of Democratic votes to move most business, hence the more conciliatory tone. But the longer-run political imperative is the same for both: They need to pivot as quickly as possible to items that can actually get signed into law, so that they have something to show the restive, angry electorate when they face them again in two years. Those likely include changes to Obamacare — there is broad, bipartisan support for repealing the medical device tax, for example. The most serious threat to the law looms at the Supreme Court, which agreed Friday to hear a challenge to the federal subsidies that help make the new insurance coverage affordable.

Meanwhile, McConnell and Boehner will need to make a show of trying to rip the law out “root and branch,” as the incoming Senate leader liked to say on the Kentucky campaign trail. For help staging the repeal kabuki, they might want to study the recent history of the opposition.

Democratic leaders faced their own version of the same conundrum when they retook control of both the House and Senate in the 2006 midterms. After twelve years in the minority, they rode back to power in part by harnessing liberal disgust with the Iraq war. That election sent a clearer message than this one, with exit polls at the time revealing 56 percent of voters disapproved of the war and 55 percent favored withdrawing some or all of the troops. And yet, with a 51-seat majority in the Senate, Democrats had little hope of forcing the hand of President Bush, who was resolute about prosecuting his surge strategy.

“We had to follow through and try to force action despite the fact that it was difficult to imagine getting the votes,” says Jim Manley, at the time an aide to Senate Majority Leader Harry Reid (D-Nev.). “It’s a release valve.”

Democrats tried to force a timeline for troop withdrawals onto funding for the Iraq war. Bush repeatedly pledged to veto it. At the end of their first year in power, with lawmakers anxious to quit the capital for Christmas, Democrats folded and approved the war money with no strings attached. Liberals fumed — “this was the time of MoveOn,” says Manley — and Democratic approval ratings dropped to 32 percent, below Bush’s own marks. Congressional Democrats turned on each other, directing recriminations at their colleagues in the other chamber. But by then, the squabbling in the Capitol was already being drowned out by a presidential contest rumbling into gear. The four Democratic Senators angling for their party’s nomination — Obama and Hillary Clinton, included — didn’t even bother coming back to Washington to cast votes. And less than a year later, Democrats rode Obama’s movement candidacy to major gains in both the House and Senate.