Recounts have to be requested on an individual county basis
Didn't Bush v. Gore I make that sort of thing unconstitutional?
In some states (such as Alabama) the primaries are still officially run by the parties or in some sort of legally nebulous partnership between the parties and the state. I'm not sure of the legal details but I think in states like that the party has far more control over the method of conducting the primary then one normally would have. But I'm just sort of talking out of my ass here.