On the NPR news this morning, I heard that the Senate Democrats are not anxious to fight for Al Franken to be seated just yet. The (currently) "final" tally has Franken winning by a preposterously small margin, and the GOP incumbent is definitely mounting a challenge.

Regarding Burris, the resistance to seating him has to do with the fact that he's Blago's appointee, not anything personal about him. If another process (probably post-impeachment, and definitely including certification by the Illinois Secretary of State) were to conclude with Burris being appointed, he'd be accepted.