What do you believe would stop them? And if you're going to say "the law" or "the Supreme Court", please quote the law or constitutional provision you feel would bar such a scenario.
Actually, I think the people, overwhelmingly, would stop them-- certainly virutally all Republicans, many Independents, and I think a good number of non-KoolAid (Zell Miller) Democrats would object to the last minute insertion of a non-vetted candidate grabbing the reins. Whatever numbers Kerry might have been polling at the time, I think a replacement candidate would get less for this very reason.
If the Lautenberg switch were played out nationally, outside of an East Coast Dem Machine stronghold, I don't think it would go over with anywhere near that kind of success.
As for the Supreme Court, they declined to intervene in the Toricelli case and overturn the NJSC ruling. That case involved an office representing the state of New Jersey, not the nation as a whole. While the Court might defer to the NJSC to interpret New Jersey law, it would not be a precedent to cover the rest of the country.