One thing I didn't know, but starting checking out on the web, is a governmental question about what happens to a Senate seat if the Senator becomes President or Vice-President?
It turns out that if a U.S. Senator wins the Presidency or Vice-Presidency, the governor of their home state appoints someone to fill their seat. The appointee will fill out that term. So, for example, Obama's seat is up in two years. So, his replacement will have the Senate seat for two years. Biden, by the way, was up for reelection and won his Senate race, so his replacement will last the full term of six years.
Evidently, the governor can choose someone from any party and does not have to replace the Senate seat with someone of the same party.
Considering that both Illinois and Delaware currently have Democratic governors, this probably will be less of an issue, but the potential is there. If there is a party-change in the governorship, the President or Vice-President-elect can resign their seat and have a replacement appointed before the governor's term is up. Or they can wait (all the way up until being sworn into office), if they are waiting for a new governor.