Congress still doesn’t seem to be buying President Obama’s argument that he doesn’t need legislative approval for the U.S. military campaign in Libya.

But, luckily for Obama, neither house of Congress seems mad enough to try to stop him.

On Tuesday, a U.S. Senate committee shot down the White House’s argument that Obama can carry out the campaign without Congress’s approval. Even after hearing a State Department attorney explain that argument — that presidents need Capitol Hill approval when sending troops into “hostilities,” but that the Libyan mission doesn’t qualify — the panel took a vote that rejected it.

But then, by a vote of 14 to 5, the same panel voted to approve a resolution that would authorize the Libyan operation anyway.

The senators voted, in essence, to give Obama the permission he says he doesn’t need.

“Congress and the president are committed to this critical endeavor,” said Sen. John F. Kerry (D-Mass.), who wrote the resolution of approval. “The United States is always strongest when we speak with one voice on foreign policy.”

It’s still unclear when the full Senate will take up the resolution that the committee passed Tuesday.

A similar resolution was voted down in the House of Representatives last week. Then, however, the House also rejected a bill that would have stripped away some funding for operations such as drone strikes and air raids on Libyan defenses by U.S. planes.

The differences between the two chambers is likely — at least in the short term — to give Obama more time to carry out the campaign. The NATO-led operation against the forces of Moammar Gaddafi depends heavily on U.S. forces for intelligence-gathering, surveillance and aerial refueling.

The committee vote to authorize the Libyan operation came after a testy morning, in which several senators criticized the arguments of State Department legal adviser Harold Koh.

Koh was there to explain an argument endorsed by Obama himself. The argument centers on a single word in the 1973 War Powers Resolution, a Nixon-era law intended to prevent presidents from sending forces into “hostilities” without congressional say-so.

Obama’s argument — as explained by Koh — was that what’s happening in Libya does not count as “hostilities.” That, Koh said, is because U.S. forces play a supporting role, there is little risk of escalation, and because Libyan forces are so battered that there is little risk they will shoot back effectively.

That argument only served to inflame legislators in the House, where several said it did not pass a “straight-face test.” It attracted similar criticism from several members of the Senate panel.

“If the United States encountered persons carrying out similar activities” in support of al-Qaeda against the United States, said Sen. Richard G. Lugar (Ind.), the ranking Republican on the committee, “we would certainly deem them to be participating in hostilities against us.”

Later, the committee approved an amendment authored by Lugar, which rejected Koh’s argument. “United States military operations in Libya . . . constitute hostilities within the meaning of the War Powers Resolution,” the amendment said.

If the resolution passed both houses of Congress, it would amount to a rhetorical swipe at Obama. But it would leave him free to pursue the same course in Libya that he is pursuing now.