Senators already divided on how to deal with U.S. involvement in Libya found themselves facing a no-win situation Tuesday: The more they struggle to be relevant on the issue, the more they highlight the futility of their fight.

The White House has asserted that President Barack Obama doesn’t need Congressional approval for the NATO-led assault against Libyan leader Moammar Gadhafi’s forces. The House already sent mixed signals Friday by failing to either authorize or defund the Libyan mission. And Senators — especially on the Foreign Relations Committee, where Members spent hours Tuesday sparring over the Libya mission — still can’t agree on what exactly is required of them.

“I have no idea why we would pass something out of Foreign Relations,” Sen. Bob Corker (R-Tenn.) said. “It’s like Congress is over here and the president has basically said, ‘Well, we can define it this way, therefore your weighing in is irrelevant unless you just want to stop it.’ And Congress is saying, ‘No, no, no! We want to be relevant. We want to be relevant! And therefore, we’re just going to pass something that supports what you’re doing.’”

In what Corker described as the “first real markup we’ve had in Foreign Relations” in four years, the panel approved, 14-5, a resolution co-sponsored by Chairman John Kerry (D-Mass.) and Sen. John McCain (R-Ariz.) that would give limited approval to the U.S. campaign in Libya. The vote came only after Kerry postponed several previously scheduled markups so he and McCain could drum up support.

But serious questions remain over the resolution’s fate in the Senate. Immediately after it was approved by the panel, Kerry said only that he “hoped” it would get a vote on the floor. A spokesman for Majority Leader Harry Reid (D-Nev.) said the Senate will not vote on the resolution before the July Fourth recess.

In a morning hearing, Kerry defended the White House and State Department adviser Harold Koh from what he called needless “dart throwing.” He said it wasn’t the president’s fault that the Libyan mission is not authorized but that the responsibility fell upon Congressional leaders, who at the time of the War Powers Act deadline were “unwilling” to bring legislation to the floor. Senate Majority Whip Dick Durbin (D-Ill.) corroborated that account, saying of the Libya conflict, “The initial signal from both sides of the rotunda was, ‘Don’t touch it.’”

But it was unclear Tuesday whether the overall will of the Senate has changed since early spring, especially in light of the divided House vote that revealed deep fissures across both parties and in both chambers.

“I don’t know the answer to that, and no one does,” Durbin said Tuesday of whether there are votes to approve a resolution. “What happened in the House of Representatives — it’s turned into a dog’s breakfast over there. God knows what their position is on this issue — to say we’re against authorizing it; we’re against defunding it. That’s why many presidents smile when they hear the words ‘War Powers Act.’”

The War Powers Act requires presidents to get Congressional approval for military campaigns that last more than 60 days, but many presidents have ignored the measure. Obama has said the U.S. involvement in Libya does not rise to the level of needing War Powers Act approval from Congress.

In its afternoon session, the panel adopted four of five amendments proposed by ranking member Dick Lugar (R-Ind.), one of the first and most vocal opponents of American engagement in Libya and a mentor to Obama on foreign policy when the president was still in the Senate.

The approved Lugar provisions would prohibit the deployment of ground forces to Libya; require the administration to report on the costs and impact of engagement to Congress; specify that the War Powers Act applies to Libya and that further action requires authorization; and render a “sense of Congress” that postwar construction costs should fall to Libya and the Arab League nations that advocated NATO’s military intervention to prevent Gadhafi from killing civilians and protesters.

“The president does not have the authority to substitute his judgment for constitutional process when there is no emergency that threatens the United States and our vital interests,” Lugar said in the panel’s first hearing. “Under the Constitution, the Congress is vested with the authority to determine which, if any, of these circumstances justify the consequences of American military intervention.”

The Lugar amendments likely made the resolution more palatable for skeptics on Libya, such as Sen. Jim Webb (D-Va.), who had co-sponsored a more critical measure with Corker but voted “aye” in Tuesday’s markup. Corker voted “no” on the amended resolution in committee.

“You cannot please everyone. The question is whether you can please the majority of people,” Senate Armed Services Chairman Carl Levin (D-Mich.) said.

Aides close to leadership say they will begin to whip the resolution in the closing days of this work period and were heartened that the 14-5 vote was not as close as they originally had anticipated.

Four Republicans voted with all Democrats to approve the resolution.