Throughout the debt-ceiling fight, Democrats and Republicans alike have argued that Washington could not — even should not — agree on a large deficit-reduction package now. A great debate, the argument goes, about the future of the country will commence in 2012. Then voters will decide once and for all which party they really want to fix America’s long-term budget problems.

This argument is obviously self-serving; it allows both parties to defer tough decisions — or compromise — until after next November, and it gives ideologues another reason to oppose cooperation with the impure. It’s also probably wrong.

Policymakers built the byzantine debt-ceiling deal that Congress passed Monday around the principle of 2012-as-ultimate-definitional-battle. Lawmakers carefully gave themselves room to continue the gridlock until then; if Congress fails to enact required new deficit reduction in 2011, it doesn’t get punished with painful, across-the-board spending cuts until 2013. Whichever party is in charge by then could rip up the whole bargain and pass another one more to its liking. And, anyway, lawmakers made the deal too small to resolve the debt question for long.

But those expecting a resounding resolution to some stark struggle of liberal versus conservative are forgetting one thing: It’s not likely to happen.

The whole argument assumes that there will be a clear winner in 2012, when it’s very possible there will be yet more divided government. The Senate math is very bad for Democrats, who have to defend 23 seats, and very good for Republicans, who only have to defend 10 seats. President Obama’s chances seem to be murkier, but considering the list of Republicans lining up to challenge him, it’s still hard to bet against the president. What if the Republicans take the Senate and the Democrats keep the White House? Utterly plausible, but whose ideology wins?

Even if one party takes control of both political branches, it’s more likely that outcome will reflect economic conditions on election day, not some new, national consensus on renegotiating the social contract that hasn’t presented itself in the previous three wave elections. These days, “mandates” in Washington come and go every two years, perhaps because they weren’t strong mandates to begin with. Believing preemtively that voters will hand down a real mandate this time around, and then legislating on that assumption, is bizarre.

Of course, the argument that 2012 will solve everything isn’t a principled one, and it’s certainly not a commitment on the part of those who make it to pack up and go home if they lose. It’s just a bet that their side can win, or that at the very least they will be able to argue that their side somehow prevailed. And, barring a truly massive electoral swing in one direction, whoever loses will still be in a position to obstruct. Which means that neither side is likely to get all of what it wants, anyway.

It’s hard to see the basic problem on the debt changing in 2012. With trillions in unfunded liabilities, study after study has found that the government needs a smart mixture of tax hikes and entitlement reforms. Republicans hate the former, and Democrats hate the latter. Both will need to compromise. Visions of a grand, ideological alignment around the next election that will spare one party from having to do so are just another excuse to delay negotiating that compromise.