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Sergey Ponomarev, Associated Press
Libyans walk past graffiti depicting Libyan dictator Moammar Gadhafi in the rebel-held Benghazi, Libya, Monday, July 4, 2011. A senior Libyan official said Monday that progress has been made in talks with rebels on ending more than four months of fighting, but a top rebel leader denied that any negotiations are taking place.

WASHINGTON — Congress is sending a muddled message on Libya to both U.S. allies and Moammar Gadhafi.

Bipartisan Senate support for giving President Barack Obama limited authority to continue military involvement against Gadhafi is at odds with overwhelming opposition in the House to the commander in chief's actions. Democrats as well as Republicans in the House have criticized Obama for failing to seek congressional consent for the operation in a constitutional stalemate that has dragged on for weeks.

In a further complication, arguments over another major issue — the federal debt ceiling and huge deficits — could sidetrack the Libya debate at any moment.

And Obama, for his part, contends he doesn't need the authorization anyway.

The Senate scheduled a vote on Tuesday on whether to proceed with a resolution authorizing "the limited use of United States Armed Forces in support of the NATO mission in Libya." The resolution would expire when the NATO operation ends or after one year, and it would prohibit the use of American ground forces or private security contractors in Libya. The Foreign Relations Committee easily adopted the measure on a 14-5 vote last week.

Leading backers of the resolution include Foreign Relations Committee Chairman John Kerry, D-Mass., and John McCain of Arizona, the top Republican on the Armed Services Committee. They have been the strongest voices in the Senate for the military action against Gadhafi's forces. Also sponsoring the resolution are Sen. Jon Kyl of Arizona, the No. 2 Republican, and Senate Intelligence Committee Chairwoman Dianne Feinstein, D-Calif.

But it could be upended Tuesday by the separate dispute over slashing spending and raising the national debt limit.

Since the Senate abandoned its plans for a weeklong recess to continue negotiations on the unresolved financial issue, some Republicans have insisted that senators focus solely on the budget. They could vote against Democratic leader Harry Reid's efforts to move ahead on the Libya resolution; he needs 60 votes to go forward on the measure.

Since NATO took command of the Libya operation in early April, the U.S. role has largely been limited to support efforts such as intelligence, surveillance and electronic warfare. The U.S. has launched airstrikes and drone attacks, flying more than 3,400 sorties.

"In Libya today, no American troop is being shot at," Kerry said last week.

But that hasn't silenced the congressional debate pitting the executive branch against the legislative.

Obama last week defended his decision to order U.S. military action more than three months ago and insisted he had not violated the 1973 War Powers Resolution, which demands congressional authorization within 60 days of first military strikes. The president contends American forces supporting the NATO-led operation are not engaged in full-blown hostilities, making congressional consent unnecessary.

Even members of the Foreign Relations Committee, which backed the resolution, rejected Obama's legal argument that the operation does not constitute full-blown hostilities. The panel adopted an amendment that specified the operation included "hostilities" that fall under the War Powers Resolution and require congressional authorization.

The sponsor of that amendment, Republican Richard Lugar of Indiana, is one of the strongest Senate critics of the Libya operation.

"Given all that is at stake in Pakistan, Afghanistan, Iran, Saudi Arabia, Egypt, Syria, Yemen, and elsewhere in the Islamic world, a rational strategic assessment would not devote sizable American military and economic resources to a civil war in Libya," he said last week. "It is an expensive diversion that leaves the United States and our European allies with fewer assets to respond to other contingencies."

In Libya on Tuesday, at least 11 people were killed in fighting that began late Monday and continued Tuesday as Gadhafi forces stepped up pressure to try to block rebel fighters from advancing toward the capital of Tripoli, rebels said.

Libyan government troops have been unable to retake two main rebel strongholds in the west — Misrata and several towns in the Nafusa mountain range. The rebels have been trying to break out of those bridgeheads.