He didn't declare war on Libya, at all. In fact, it wasn't even him that proposed the idea of the no-fly zone to the UN, but it was the Arab League. The UN security counsel was waiting for the US to agree on the no-fly zone, and Obama eventually relented & agreed. War wasn't declared, considering the fact that he hasn't sent troops onto Libyan soil, and is only assisting the rebel opposition by helping take out AA-guns. If anything, the British and the French are launching more airstrikes than us.