The wikipedia article on the war is somewhat confused, but it states that NATO troops were (also) a NATO demand, and that the Serbian counter-proposal was unacceptable even to the Russians.

The initial target list, I believe, was the substance of much political discussion, with the French and Italians initially blocking much of the targets that the US wanted to bomb, and gradually being convinced to allow for an expansion. NATO was made up of many countries with different positions, and the development of the war has to be seen as a matter of compromise internationally and also nationally (between Clinton and a Republican Congress).