The states can set their own deadlines, but all states operate under the assumption that each state won't mess with the rules once their legislatures write them. That is the equal protection.
-PJ
Nope. The seat is for a New Jersey Senator and is only up to New Jersey voters. They are the only voters to be considered. An equal protection claim would have to argue that some portion of New Jersey voters is being treated differently than the other New Jersey voters.