Without NASA contracts (to be noted: fixed price contracts predicated on delivery of goods, for the most part) SpaceX would have much less cash on hand and their pace of R&D would be much slowed. But they would still exist and still be pushing the state of the art, just at a slightly slower pace. They have one of the most competitive orbital launchers on the market, they have a ton of commercial business already on the docket, and the next 3 SpaceX launches are, in fact, non-NASA commercial flights (a Canadian weather satellite, a commsat for servicing East Asia and Oceania, and several Orbcomm commsats).
