But did the process at least help President Obama's prospects for reelection, as the White House hoped it would? Hardly.
When Boehner walked away, Obama and his aides consoled themselves with the notion that the president could cast himself as the only responsible adult in the room, mediating among small-minded politicians in the nation's interest.
But that didn't work either. Senate Republican leader Mitch McConnell, who says defeating Obama is his priority, had no interest in helping the president look good. McConnell made a point of negotiating with Vice President Joe Biden and Senate Democratic leader Harry Reid, not Obama, and it was those talks that led to the eventual deal.
At the end, of course, Obama was in the room. But much of the time, he looked more like a victim than a hero. When his talks with Boehner failed, the president described himself as a forlorn bride, "left at the altar." Rep. Charles Rangel (D-N.Y.) said Obama had simply been mugged. As appeals for sympathy, both images had a certain charm, but they didn't do much for the president's stature.
Opinion polls confirm that Obama didn't gain ground in the eyes of the public, although he didn't lose any, either. Gallup polls over the three days since the debt-ceiling deal was announced put Obama's approval rating at an anemic 42%, just about where it was before.
Democrats have tried to console themselves by noting that the deadlock drove the popularity of Congress and its Republican leaders even lower than Obama's. Gallup said Congress' standing has hit an all-time low, with only 14% of the public approving of the legislators' performance.
But that won't do Obama much good next year. He's not running against John Boehner; he's likely to be running against a governor who never got near Capitol Hill. In one poll released this week in Pennsylvania, which Obama won handily in 2008, Republican front runner Mitt Romney is running even with Obama. Romney stayed so far away from the mess in Congress that he refused even to take a position on the debt ceiling until the very end; that doesn't appear to have hurt him much.
Obama has suffered, in part, from a clarity gap. Even his own supporters aren't always sure what he's willing to fight for.
"He needs to plant a flag somewhere," complained William A. Galston, a former top aide to then-President Clinton. "I don't care what color it is. But periodically planting a flag and then lowering it is no way to inspire confidence."
The president took a clear position on only one issue in the debt ceiling negotiations: He said any deal had to be "balanced," meaning it had to include new tax revenue as well as spending cuts. But in the face of Republican opposition, he backed off even that one demand.
Obama's negotiating victories in the final deal weren't on matters of substance, like tax revenue. They were on matters of process: on making sure another debt-ceiling vote doesn't happen until 2013 and making sure the mechanism for choosing further spending cuts isn't tilted in the Republicans' favor. Try selling those to voters as a victory for the beleaguered middle class.
Republicans, on the other hand, suffered from an excess of clarity. They had just two major goals: deep spending cuts and no new taxes. On taxes, they stuck to their guns and won. On spending, deficit hawks complained that the cuts weren't deep enough, but they were enough for Boehner and his lieutenants to claim at least a partial win on their top priority.
Obama and his aides are now hoping to change the subject to something they want to talk about more than debts and deficits: job creation. They plan to ask Congress to extend long-term unemployment insurance, renew a payroll tax cut and fund an "infrastructure bank."
The idea is to propose measures that could inject one more mini-dose of stimulus into the flagging economy, measures that will be hard for many Republicans to oppose (except for "tea party" Republicans, of course). They'll force the GOP to debate Obama on his own ground — unlike the debt ceiling, which was mostly fought on Republican ground.
They're also ideas that belatedly borrow a lesson from Bill Clinton. They're relatively modest programs, measured in billions, not trillions. And they have the virtue of clarity; they're easy to understand.
But, as Obama has discovered before, keeping Congress focused on the agenda of his choice is easier said than done.
Besides, the debt ceiling debate isn't over; it's merely gone into remission. Meanwhile, Congress still has to decide on federal spending levels for next year by Oct. 1. And Congress' new "super-committee" is supposed to recommend more spending cuts by Thanksgiving.
They are all ways of posing the same core questions: How big a federal government do we need, and how do we want to pay for it?
Republicans have given answers that many voters find extreme, but at least they're clear. If Obama hopes to keep his job, he will need to match their clarity.