Top Senate Democrats defended the administration’s handling of the crisis in Libya on Wednesday and predicted that President Obama would win bipartisan backing for the military intervention there if it comes to a Congressional vote.

In a conference call with reporters, Senator Carl Levin, the Michigan Democrat who is chairman o the Armed Services Committee, also said he had asked the Pentagon and his staff to assemble an estimate of the costs of the operation. He said he expected American military forces to hand off responsibility for enforcing the no-fly zone in a matter of days, not weeks.

Mr. Levin was joined by Senator Richard J. Durbin of Illinois, the No. 2 Democrat in the Senate, and Senator Jack Reed of Rhode Island, a former Army officer, in pushing back against bipartisan complaints from Congress that the president had not sufficiently consulted with lawmakers before initiating military operations in Libya.

“He has proceeded in a way that is cautions and thoughtful,” Mr. Levin said. “He has put the ducks in a row before he decided the United States should take the lead for a short period of time to do what only we could do.”

With Congress returning next Monday from its weeklong break, the lawmakers said they could not yet say whether a floor vote would be taken on the role of the United States or if American forces would still be deeply involved in Libya. But they noted that a Congressional vote was possible, with Mr. Durbin saying he supported the right of Congress to assert its constitutional role.

Should a vote occur, Mr. Levin said, “I think the president will gain bipartisan support for his action.”

The lawmakers were unable to estimate the cost of the operation or how the price tag would figure into the ongoing debate over spending cuts or the budget for the next fiscal year. But Mr. Reed noted the costs would be less than if the United States had acted on its own.

Mr. Durbin said that he believed he had been kept up to speed on developments in Libya but that Congress would receive much more information when it reconvenes.

“Trust me, when we return this week I am sure we will have a complete briefing from the administration on this entire situation,” he said.

Mr. Levin said an already scheduled hearing in his committee on Tuesday would also serve as a Congressional forum on the Libyan operation.