I'm pretty sure that it's enshrined in N.H. law that their primary is held a week before any other, and not necessarily on a specific date. (This doesn't seem to apply to caucuses, for obvious reasons.) Therefore, it doesn't seem likely that it'll happen any time soon.
If that actually is the case re: New Hampshire, then what would happen if another state passed the same law?
Probably the two states would keep trying to schedule their primaries ahead of each other ad infinitum. However, such laws are actually meaningless in that the national parties don't have to seat the delegates elected in these primaries if they don't want to. So NH can schedule an election for whenever it likes, but the national parties can simply impose rules that prevent the election from counting towards the nomination process if it takes place too early. And in fact, this is exactly what's happened.
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