It is definetely a (big) part of the reason, but if it was the only one, things wouldn't be in a similarly terrible situation in other countries. Take the UK as an example which has a single-payer system, and morale is overall really low, too, and nursing isn't an enticing career. (On a side-note, the BBC show "This is going to hurt" is quite good and on topic)

Apart from administrators and insurers, I think a large problem is that the job has become substantially more difficult and technology intense, while support and pay hasn't kept pace. At the same time, liability is more serious these days, which I don't think is a bad thing, but certainly sucks for the workers who have to constantly justify themselves and can get crucified for mistakes.