Barack Obama is betting his presidency on the hope of cooperation from an institution that he disdains and has proved incapable of taming. His roll-the-dice gamble for congressional go-ahead in Syria may well succeed. Still, the risk is enormous for Obama’s fraying credibility, and the implications are significant not only for the power of this president but for his successors.

Obama’s decision to seek congressional approval was sudden, verging on erratic. He was certainly correct when he said Saturday that “our democracy is stronger when the president and the people’s representatives stand together.”

But that raises an uncomfortable question: Why didn’t the president plan to seek authorization from the start? How can this request to Congress be reconciled with Obama’s willingness to act unilaterally in Libya — indeed, to argue that, months after the operation began, he did not need congressional authorization because the bombing campaign did not amount to the kind of “hostilities” contemplated by the War Powers Act?

In shifting course, the White House — or, more precisely, the president, since much of his staff was understandably skittish about seeking congressional support — was influenced by the British experience. Parliament’s rebuff of Prime Minister David Cameron’s request for approval to intervene in Syria put the White House in a difficult position, making it look as if democracy was fine for the United Kingdom but too dicey for the United States. Meanwhile, the blowback from Congress and the public has been fiercer than the White House anticipated.

Obama couched his decision in high-minded terms, as “president of the world’s oldest constitutional democracy” and a believer in government by the people. But numerous members of Congress, including some of his own party, sniffed a less lofty motive — seeking political cover for an unpopular move.

The White House and its allies promptly reinforced those suspicions. “Congress is now the dog that caught the car,” former senior adviser David Axelrod tweeted Saturday. The Post’s Scott Wilson quoted an unnamed aide making a similar point about congressional second-guessing: “We don’t want them to have their cake and eat it, too.”

Really? What is the president doing when he asserts the authority to carry out military strikes without congressional approval, says he has already decided on such action and won’t address what he might do if Congress declines? Seems there’s an awful lot of cake-eating going on.

Having said he wanted an operation “limited in duration and scope,” Obama presented Congress with a draft resolution breathtaking in its absence of limits. It would empower the president to use the military “as he determines to be necessary and appropriate in connection with the use of chemical weapons” in Syria.

Whoa! No time frame. No ban on ground troops. Senator Obama would never have voted for what President Obama proposes. The White House no doubt figured that it should ask for the maximum authority possible, rather than negotiating from a middle-ground position. But, like the seller of a house who initially prices it way too high, the administration may end up getting less than it might have with a more reasonable starting point.

Tuesday’s news was positive for Obama, with Republican and Democratic House leaders backing a military strike. Still, three possible outcomes remain, two terrible and one worrisome.

First, Congress balks and Obama backs down, shredding his remaining credibility but avoiding a constitutional and political showdown.

Second, Congress balks and Obama proceeds nonetheless, enraging lawmakers and eroding what capacity remains for legislative accomplishment.

The third possibility — Congress agrees — is the preferable outcome but not without some peril. Every such episode sets a precedent that presidents current and future must grapple with, if not obey, in managing the delicate constitutional balance between the congressional war power and the president’s role as commander in chief.

As David Rothkopf pointed out in Foreign Policy, Obama — having expanded the boundaries of presidential power in Libya — has now boxed himself in, making it “highly unlikely that at any time during the remainder of his term he will be able to initiate military action without seeking congressional approval.”

And future presidents will, similarly, be called on to explain any noncompliance with the Obama precedent. This may be good or bad, depending on whether you more fear a reckless president unbounded by congressional supervision or a hamstrung president shackled by a dysfunctional Congress. But it is another reason why this last-minute move is so momentous.

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