Let's forget for a moment that none of this was approved by the internationally recognised government of Libya.

It isn't just the United States that has invaded Libya. British forces are on the ground in Libya.

Britain has discreetly deployed military advisers to Libya in order to build an army to fight Islamic State of Iraq and the Levant cells in the country, The Sunday Telegraph has been told.
Special forces commandos are said to be working alongside their US counterparts in the city of Misrata to stop the jihadists’ progress in the lawless terrain across the sea from Italy.
Even as diplomats in Washington, London and European capitals push for the formation of a unity government in Libya, US military operatives have begun “giving tactical training” to select local militias, Western officials, US congressional aides and sources on the ground have revealed.

Even before British forces invaded Libya, the French were already there.

French special forces have been helping Libyan troops fight Islamic State militants in the eastern Libyan city of Benghazi for two months, two Libyan military officials said Wednesday.
According to the officials, the French forces were setting up an operations room in Banina air base in Benghazi alongside British and U.S. teams. They said that in addition to the special forces, a French intelligence unit is working with Britain and the U.S. units to collect information on the location of IS militants and their numbers.

Italy was asked to join, but declined. Maybe the neocolonial look of this intervention was just too much for Italians, but they did agree to host our drones.

The Italians granted permission for the drones to be used only defensively, to protect U.S. special-operations forces in Libya, the officials said.

Before British and French troops, there were American troops in Libya.
So far these special forces groups have been very small, but then we were only going to send a few hundred troops back into Iraq too.

The question is: how long can Obama keep this invasion on the DL?

The President wants to play down this new Libyan war because it would be another admission of failure. So add Libya to the rising tide of war this President will leave to his successor.