Well, for the California example, CalTrans is the govt. They're well staffed and don't (generally, it may occur occasionally) rely on contractors for their work. I believe the same goes for CDOT and other agencies, though many of them are more willing to contract out as they don't necessarily prioritize roadwork like Californians do (for obvious reasons).
Generally, it's particularly rare (at least in the Western "blue" States) to rely on mostly or, especially, exclusively private public works programs.
Generally, it's particularly rare (at least in the Western "blue" States) to rely on mostly or, especially, exclusively private public works programs.