Get right down to it, the War Powers Resolution, as Pro Publica points out, is on shaky ground and always has been, "always" meaning from its 1973 passage to present.
The law was passed in 1973 after the United States fought the Korean and Vietnam wars without actual declarations of war. But it’s always been controversial. (President Nixon actually vetoed the law, but Congress overrode him.)
According to a 2004 Congressional Research Service report, “every President since the enactment of the War Powers Resolution has taken the position that it is an unconstitutional infringement on the President’s authority as Commander-in-Chief.”
Which isn't to say that the War Powers Resolution hasn't been useful as a bludgeon if Congress chooses to use it against the president.
As Marian Fang, at Pro Publica points out, this president hasn't used the counter-argument about executive privilege. Obama's point is that the administration isn't in violation of anything.
White House spokesman Jay Carney has argued that the United States’ “constrained and limited operations” in Libya “do not amount to hostilities” because the United States doesn’t have or intend to place soldiers on the ground and has not sustained the casualties typical of such hostilities.
That gets up John Boehner's nose as can be expected. He doesn't buy the argument that's it's NATO's war and we're lending men and materiel but not soldiers "on the ground." Boehner's former party leader, George W., signed the damn thing after all, but protested it was unconstitutional.
"As I made clear to congressional leaders at the outset, my request for congressional support did not, and my signing this resolution does not, constitute any change in the long-standing positions of the executive branch on either the President’s constitutional authority to use the Armed Forces to defend vital U.S. interests or the constitutionality of the War Powers Resolution."
The bottom line is, of course, Qaddafi's departure. There's a fixed goal, the US has undertaken the responsibility to support the effort to "persuade" Qaddafi and his kin that their authoritarian days are over. Most Americans can relate to that. Boehner can play chigger or rattlesnake in this, but he may well recognize already that he's not on solid ground either politically or constitutionally.
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Legal scholar Rick Pildes makes an interesting point. The 60 days have come and gone.
By design, the WPR makes Congress’s silence – its failure to act to take any position one way or the other about the Libya operation – tantamount to a decision by Congress to prohibit the United States from participating in “hostilities” in conjunction with the Libya operation. Thus, Congress’s failure to act has all the consequences, as a practical matter, of an affirmative decision by Congress to cut off the Libya operation, though without Congress actually making such a decision or having to take direct responsibility, through the act of voting, for such a decision and its ensuing consequences.
That's not going to stop any arguments, but they'll be political arguments. As one commenter points out, no court would hear a dispute between the president and Congress, but "if the WPR was re-worked with a one-house veto provision, there could be alternative enforcement mechanisms, such as congressional rules that would lead to a cutoff in funding."
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The New York Times (6/18/11) looks at the wide area of disagreement on the issue of whether the President has had legal authority to "continue American participation in the air war in Libya without Congressional authorization."