To conservatives, this has been a galling spectacle. A president who spent his first two years in office taking spending to a historic high is accusing them of fiscal irresponsibility? A president who spent the spring demagoguing House Republicans for their willingness to restructure Medicare is citing a much more modest set of cuts as evidence of his fiscal seriousness?

But this fury misses the point. Obama has been playing the reasonability card so successfully because his opponents won’t (or can’t) play one of their own.

It’s not that Republicans needed to tug their forelock and go along with whatever grand bargain the White House whipped up. But to win the endgame, they needed something they were willing to concede, something they could tout in public as an example of meeting the Democrats partway.

Their inability to make even symbolic concessions has turned a winning hand into a losing one. A majority of Americans want to close the deficit primarily with spending cuts — which is to say, they’re primed to side with conservatives in the debt-ceiling debate. But in trying to turn that “primarily” into a “completely,” the right has squandered this advantage. By 48 percent to 34 percent, a Quinnipiac poll found last week, Americans will blame Republicans if debt-ceiling gridlock precipitates an economic crisis.

In the end, the threat of such a backlash will probably impel Republicans to make some kind of concession anyway, if they don’t admit that’s what they’re doing. (The maneuver that Mitch McConnell and Harry Reid are working on, for instance, would reportedly cut spending by $1.5 trillion and then let the president extend the debt ceiling on his own, effectively shaving about $500 billion off the spending cuts that Republicans were originally seeking.)

By backing into a compromise and shrouding it in procedural gimmickry, Republican legislators may hope to throw the Tea Party’s watchdogs off the scent. But both the politics and the substance of such a deal would probably be worse for conservatives than the kind of bargain that might have been available otherwise — if more Republicans had only recognized that sometimes a well-chosen concession can be the better part of valor.