As I suspected would happen, the U.S. Supreme Court declined to get involved in the New Jersey Senate race ballot dispute, as did a federal district court. The Republicans had a couple of reasonable arguments, but I think the Democrats had the stronger position on this one point, from their Supreme Court brief:
The Applicant has failed to meet his burden of proving irreparable harm in every way. He alleges no harm of his own, and he shows no real potential of harm to others – except Senator Lautenberg and the Democrats of New Jersey. Given that there is currently no voter from the State of New Jersey whose ballot condition will not or cannot be fixed over the next month, there is no need for this Court to intervene.While Doug Forrester's election chances were seriously harmed by this decision, that's not the kind of harm the court is going to rectify. That doesn't mean I agree with the Democratic position, though. The real harm was not to Forrester, but to the rule of law. It sounds reasonable to say that statutes should be interpreted "liberally" in order to preserve voter choice. Why let some minor technical administrative details get in the way of a full electoral process? Why? Because that's the law. It's true that rules can sometimes operate in ways that seem rigid. But there's an advantage to "rigid" rules that doesn't apply when one construes the rules "liberally." There's no possibility of bias. Exceptions aren't made by formula; human beings have to decide to grant exceptions. And those people aren't deciding in a vacuum; they know the effects of their decisions when they make them.
When the legislature wrote the law in question, they didn't know whether a Democrat or Republican would benefit. They didn't know whether the Senate would be closely divided. Their choice of a deadline, while arbitrary, was unbiased. When the New Jersey Supreme Court rewrote the law in question, they knew they were benefiting the Democratic Party. There's just too much temptation for abuse. There's the appearance of impropriety, even if the judges are trying to be fair. All we have to do is look at Bush v. Gore to see this problem. Republicans were convinced the Florida Supreme Court was biased. Democrats were convinced that the U.S. Supreme Court was biased. And it was all because people were ignoring the law in favor of ad hoc decisionmaking.
Aside from that, when exceptions are made, its inevitable that they'll be made to benefit the powerful, not the weak. Does anybody believe that the court would have extended the deadline for the Socialist Party, or the Libertarian Party, or the Greens? (In this case, the New Jersey Supreme Court even admitted it: this decision was made in part as part of a policy "to preserve the two party system.")
Pre-established rules, no matter how arbitrary, treat everyone equally. Exceptions don't. Exceptions can't.