What happens in Libya when the shooting stops?

(CNN) -- There was never much doubt that the U.S.-built military coalition would quickly seize control of the skies over Libya. The real questions surrounding this are why the action was taken and what its ultimate political and diplomatic goals are.

The specific goals of what Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, called a "limited" military mission are to create a no-fly zone, protect civilians from attacks by forces loyal to Col. Moammar Gadhafi and allow humanitarian support to proceed in Libya, he said Sunday on CNN's "State of the Union."

"We would like to see (Gadhafi) withdraw his forces across the country back into garrison" and stop attacking his people, Mullen said.

Violence has raged in Libya following protests calling for democracy and demanding an end to Gadhafi's almost 42-year-long rule. Rebel forces, based in the eastern city of Benghazi, pushed west toward the capital, Tripoli, before being pushed back by the superior firepower of the Libyan military.

As those forces bore down on Benghazi last week, Gadhafi vowed to go house to house to "cleanse" the city of opposition members.

That threat, along with some American persuasion, prompted the U.N. Security Council to pass a resolution authorizing the implementation of the no-fly zone. The move came with the unprecedented support of the Arab League.

The Security Council resolution cited "the gross and systematic violation of human rights, including arbitrary detentions, enforced disappearances, torture and summary executions" reportedly being carried out by Gadhafi's military against people in opposition-held areas. It also took pains to emphasize the desire to "find a solution to the crisis which responds to the legitimate demands of the Libyan people."

"By employing genocidal threats to 'cleanse Libya house by house,' (Gadhafi) forced the world community's hand in taking strong action to protect the human rights of all Libyans," wrote Romeo Dallaire and Jeffrey Bernstein on the website of Foreign Policy magazine. Dallaire is a Canadian senator and was force commander of the U.N. peacekeeping mission for Rwanda in 1994. Bernstein is Dallaire's project officer for genocide prevention.

Both President Barack Obama and Secretary of State Hillary Clinton have said in the past two weeks that Gadhafi should give up power, but administration officials and Democratic senators insisted Sunday that regime change was not the goal of the military mission.

"The goal of this mission ... is not to get rid of Gadhafi," Sen. John Kerry, D-Massachusetts, said on NBC's "Meet the Press." "That's not what the United Nations licensed, and I would not call it going to war. This is a very limited operation that is geared to save lives, and it was specifically targeted on a humanitarian basis. ...

"We're not policing Libya," he added. "We are engaged in a humanitarian initiative to prevent the slaughter of innocent people, to prevent a dictator from dragging people out of hospital beds and they disappear and he kills them, to ruling his country by pure force when there is an indigenous movement to try to join with the rest of the countries in this Arab awakening that is taking place."

But others argued that ousting Gadhafi is exactly what the goal should be.

Sen. Lindsey Graham, R-South Carolina, and a member of the Senate Armed Services Committee, said on "Fox News Sunday" that this is the "best chance to get rid of Gadhafi in my life."

"If we don't get rid of him, we will pay a heavy price down the road," Graham said.

Directing his words to Obama, Graham said: "Get rid of this man. Don't be uncertain in your statements. Be bold, be effective, work with the international community. Replace this international outlaw sooner rather than later."

Independent Sen. Joe Lieberman of Connecticut said, "We can't afford to let (Gadhafi) stay in office."

"If Gadhafi survives, the Arab spring maybe comes to too-soon an end, at least it doesn't move beyond Tunisia and Egypt," Lieberman said on CNN. "It's late, but it's not too late, if we act quickly together."

But the Russian Foreign Ministry on Sunday warned against going "beyond the intended goals of the resolution, namely the protection of the civilian population."

Russia was one of five Security Council members to abstain on the resolution, which passed 10-0 on Thursday.

Critics are also wondering why the Security Council and the Arab League haven't seen fit to take similar action against other countries experiencing internal political strife, such as Syria and U.S. allies Bahrain and Yemen.

"If any lesson should be learned by any of us from what happened in Tunisia and Egypt, it's that you cannot forever suppress the desire of your people to be free and have opportunity, economic opportunity," Lieberman said.

"And so I regret what our friends in Bahrain are doing now. I hope they stop it and that they enter once again into peaceful negotiations with their opposition to create a better future for their country."

Micah Zenko, fellow for conflict prevention at the Council on Foreign Relations, wrote on Foreign Policy's website: "There are plenty of conflicts that are far more -- or at least equally -- pressing. In October and again this spring, for example, the African Union requested a no-fly zone from the U.N. Security Council to patrol Somalia. Guess how many French and British planes are flying over Mogadishu today? None."

The difference is the man at the center of the story in Libya, said Ali Suleiman Aujali, the former Libyan ambassador who defected two weeks ago.

"The danger is Gadhafi himself," Aujali said on ABC's "This Week."

"The great irony was almost in the same week that Saudi Arabia and the (Gulf Cooperation Council) countries and the United Arab Emirates backed the use of force through a no-fly zone in Libya to back the protesters, they decided they would intervene in Bahrain against the protesters, on almost the same day," Robert Malley, Middle East and North Africa program director at the International Crisis Group, said on CNN's "State of the Union."

"I mean, I think ... there is a difference, not only because of the U.N. Security Council resolution, but (also) because of the degree to which Col. Gadhafi had been using force against his own people," Malley continued.

"But these contradictions are going to be extremely difficult to navigate. Take the case of Yemen, where over 40 people were killed just two days ago. ... It's going to be very hard for these countries to remain consistent."

Sen. Jack Reed, D-Rhode Island, acknowledged what might be the unspoken objective of the coalition.

"Hopefully, they will eject Gadhafi from power, but also coordinate with the elements in opposition and try to develop a stable government," he said on "Fox News Sunday."

"But he's a thug; he's a cagey guy; he's a survivor. We know that," Mullen said on CBS' "Face the Nation." "So it's difficult to know exactly how it comes out. But in the immediate future we're very focused on protecting, providing the environment in which the Libyan civilians cannot be massacred by him and that there can be humanitarian relief, particularly in and around Benghazi."

Sen. Richard Lugar, R-Indiana, the Republican leader of the Foreign Relations Committee, expressed worry about a Middle East quagmire for the United States.

"We had better get this straight from the beginning or there is going to be a situation in which war lingers on, country after country, situation after situation, all of them on a humane basis, 'saving people.' All maybe with the Arab League in or out of it," he said on "Face the Nation."

The International Crisis Group's Malley said the world needs to think through every potential scenario in Libya, including the possibility that Gadhafi digs in and the country ultimately is partitioned.

"One thing I've learned over the past two weeks is you don't make a prediction, because you're going to be immediately contradicted the next day," he said on "State of the Union." "I mean, this is a region that is in such torment that for anyone to try to assume what the next step will be is really taking a big, big gamble. ...

"We know what we're trying to prevent. It doesn't mean that we know what we're trying to achieve."