As the recent Caroline Kennedy and Rod Blagojevich sagas illustrate, there's a huge problem with the laws regarding Senate succession in many states.
I have an issue with a single person having the power to appoint the successor to a Senator should he or she leave office before the end of their term. In relation to the national political landscape, it can have a profound effect on the balance of the Senate. When the will of the people can be easily subverted by the vote of just one governor, we need to take a long look at how to fix the problem.
This isn't simply a problem for Democrats. There are currently 58 Democratic senators; actually 59, since the Minnesota recount is almost definitely going to Franken. Should a Republican senator leave office in a state with a Democratic governor, the vote of just one person would create a super-majority in the Senate and have far reaching implications until the next general election. It wouldn't matter if the departing senator won by a landslide, it's up to the will of the governor who to appoint, even himself.
Plus, as Blagojevich shows, the possibility of corruption may unduly influence the decision.
With Caroline Kennedy, you have a recently ascended NY Governor who is being put in a very difficult position. The Kennedy name is very influential, and David Paterson may conceivably risk his future political health if he doesn't present Ms. Kennedy with the seat, even though she's never even campaigned for public office, let alone served in an elected position. She is completely unvetted in the traditional sense, such as campaigning for the requisite 18-24 months to gain the opportunity to be placed on the ballot. She hasn't even had a press conference yet, unless you consider her one-sentence statement last week with no questions allowed to be a press conference.
I've always been in favor of total Democracy. Anything that puts the power into the hands of the people when filling vacant seats is a good thing. I think we need to examine the laws regarding succession of this national office, and pass some sort of law that requires a special election within a reasonable amount of time, perhaps no more than 60-120 days after the office becomes vacant. If a primary is needed, a month or so would be minimally enough to at the very least introduce the candidates to the public.
The point is, while there's no simple solution to this, ANYTHING is better than the decision being made by just one vote, without recourse, cast by a single person.