It can be safely said that the US role was crucial. This is because it is the US who determines the foreign policy of NATO and its members in most important respects.
It is hardly possible that a US-affiliated country begins bombing or invasion in other countries without consent and support from the US.
The US was leading the diplomatic pressure on Libya. It was also behind the notorious UN resolution. It put pressure on Russia, China and Libyan neighbors so that they ceased support for Libya.
It was the US who organized the initial anti-government riots in Egypt and Libya through US-supported and instructed political activists. Note that the "Arab spring" protests starting from Egypt even used the flags with international logo of the "color revolutions" - the black fist on the white background, which has been featured in the French film "Revolution.com - USA: The Conquest of the East".
The USA was also among the first governments to recognize the rebel government.
Regarding the US share in the NATO-conducted military operation and military defeat of the government forces, the US contribution was also high. The planes which bombed Libya were launched from the US carriers, US provided infrastructure, coordination, nintelligence, planning and communications for NATO.
Besides this, it closed all satellite communications channels to the Libyan government and shipped weapons to the rebels.