Ignoring the questions of legality, morality, economic sense, and possible political opportunism that many have already touched on in President Obama's decision to go to war with Libya, there remains the question of what, if anything the no-fly zone is meant to accomplish.
If the goal is to prevent Gaddafi from using aircraft against the rebel forces, then there is reason to believe that this operation will be successful. If instead, as Obama is now saying, the current goal is that “Gaddafi needs to go,” a no-fly zone will be completely ineffectual. Despite Obama's promise for a limited military engagement, and use of political tools such as sanctions to force Gaddafi to leave, the only way to truly ensure a regime change would be a massive escalation of force beyond what a no-fly zone provides.
Conventional military combat requires both air and ground, and to a lesser extent naval, forces to properly secure another nation. The whole purpose of acquiring air superiority is to ensure that friendly forces are supported by aerial bombardment and reconnaissance. An air force can indeed patrol the skies and prevent other planes from launching, but unless those air forces are willing to engage ground forces, then they are severely limited in their effectiveness in supporting friendly ground troops.
Obama has been sending mixed messages about our goals in Libya. He keeps saying he wants Gadhafi gone, which strongly implies that this is the real goal of the current operations. This is probably a better goal than a no-fly zone, which by itself would probably create a stalemate on the ground and an endless conflict.
The ouster of Gadhafi will require a ground force to march on the palace and occupy the city while a new government is formed. The logical choice of forces to do this would the be the rebels. But their strength and skills so far suggest they cannot do this on their own. The rebels, in essence, are simply untrained civilians. Asking them to march on a city, even if we armed them, would be unreasonable. Even professional armies have trouble taking and clearing cities.
But Obama has claimed, the U.S. is in a limited military role as laid out by the U.N. resolution, a resolution that does not provide for U.S. troops on the ground.
So what other methods are there?
The use of non-combat methods to oust Gaddafi, such as sanctions, have been brought up. But these programs have never been particularly effective in the past. A quick glance through the countries currently under U.S. sanctions reveals nations such as Cuba and Iran that have been under sanctions for decades with no effect on their leaders' hold over the people.
Other nations seemingly understand the limited capabilities of political tools and a no-fly zones. They have worked on escalating their capabilities beyond simply preventing Libyan aircraft from launching. The U.K. has had special forces on the ground since near the beginning of the conflict while French aircraft have actively engaged tanks crewed by Gaddafi loyalists.
President Obama has enacted a state of war with Libya using methods that cannot meet his intended goal. If the President is intent on following through with his words and ousting Gaddafi, it will mean Obama must commit forces beyond what a no-fly can accomplish.