[Cooter]

Actually, the appointment would only last until November 5. The winner of this election would then become senator immediately.

[capitan_refugio]

When a person is elected Senator in a special election, they can assume the seat (if they are not already holding it) as soon as the election is certified. Since this is an election for the seat in its normal cycle, the Senate does not necessarily have to accept the Senator-elect until the beginning of the new session (although it has been customary to do so). In the US Senate, the Senator-elect is required to "present his/her credentials."

Each house of Congress has Constitutional authority to determine their own membership. They can throw members out and refuse to seat potential members for cause. The last time this happened in the Senate, I believe (and this is from the cobwebs of my memory of US history), was back around the time of post Civil War reconstruction.

If the Republicans win a sufficient number of seats in the Senate to form a clearcut majority, they could conceivably refuse to seat Lautenberg, if Lautenberg wins. They could instead seat the legal candidate who received the highest number of legal votes. There is no judicial review of this process.

Of course, such a move would require the new Majority Leader to actually have some vertebrae.