Since the Constitution gives the states the right to decide who will represent them in Congress, I see no real problem with governors being allowed to appoint interim Senators, to fill mid-term vacancies, if that is what the citizens of a state wish.   However, I think generally the citizens of a state would be better served if a) such an appointment had to be from the same party as the departing Senator (except maybe in the case of impeachment), and b) the state legislature could veto such an appointment with, say, a 60% vote.

As for Burris, I kind of feel sorry for him, but I think in the interest of his state, his party, and perhaps the country, maybe he should resign. His appointment has been contaminated by his contacts with the disgraced and corrupt Blagojevich. Moreover, he is very likely not only not to be elected Senator from Illinois when his interim term expires but, in effect, to hand that seat to a Republican.   If nothing else, his age weighs against his chances. If the current Illinois governor is allowed to appoint someone else, I think he is likely to appoint someone with a much better shot at holding that seat for a while.

Burris could resign and still hold his head high, much as Bill Richardson withdrew from consideration as Commerce Secretary, to avoid entangling his party and the country in a protracted "distraction."