But Obama said that in just 10 days his administration has fulfilled its pledge to the American people to keep a limited role for the U.S. military by focusing "unique capabilities on the front end of the operation" and then transferring responsibility to international allies.
The president outlined the buildup to the military intervention earlier this month and gave a status report on what has happened in the past 10 days, declaring the efforts a success.
But when it came to a timetable for U.S. involvement, he provided no specifics.
"Going forward, the lead in enforcing the no-fly zone and protecting civilians on the ground will transition to our allies and partners," he said. "I want to be clear: The United States of America has done what we said we would do. That is not to say that our work is complete."
Acknowledging that Americans have questions about the endgame in Libya, Obama said the United States will help transition to a "legitimate government" but that, ultimately, it is a task for the international community and the Libyan people.
Americans are particularly leery after nearly a decade of military engagement in Iraq and Afghanistan. Budget watchers say the first week of bombing and air support in Libya cost more than $600 million.
"If the American people are uncertain as to our military objectives in Libya, it is with good cause," said Sen. Mitch McConnell, the top Republican in the Senate on Monday. "The president has failed to explain up to this point what follows the evident establishment of a no-fly zone over Libya as it was originally described. Further, the president has articulated a wider political objective of regime change in Libya. That is not the stated objective of our military intervention, nor is it the mandate of the UN resolution that the president has used as a justification for our military efforts there."
NATO is set to take over command of the operation, but the Americans Navy and Air Force are still very much involved enforcing a no-fly zone over Libya.
The full transfer of command to NATO will be complete in several days.
But Defense Secretary Robert Gates would not give a firm deadline for just how long U.S. involvement would last. "Will the mission be over by the end of the year?" he was asked by ABC's Jake Tapper on Sunday. "I don't think anybody knows the answer to that," Gates said.
Establishing the no-fly zone is described as a humanitarian effort, authorized by the United Nations Security Council, to keep Gadhafi from slaughtering rebels who hope to push him out of power.
"Imagine we were sitting here and tens of thousands of people had been slaughtered. The cries would be, 'Why did the United States not do anything?'" said Secretary of State Hillary Clinton on ABC's "This Week" Sunday.
But the aim of the U.S. is not just to keep Gadhafi's give the rebels a fighting chance. At the same time, President Obama said Gadhafi must leave power. The distinction between avoiding a slaughter of civilians and working to oust him has created a great deal of confusion about what the U.S. and its European allies are trying to accomplish.
To critics who have argued that Obama and the international coalition should be doing more to bring down Gadhafi, the president said broadening the mission to include "regime change" would be a mistake.