This is not so surprising. He promised before the arrest to fill the seat by Christmas, and he's only a few days late. I think that White and Reid have little choice but to object, and let the courts force them aside.
Indeed, White and Reid will be shoved aside by the courts if Blago and Roland truly wish it (I suspect Burris would step aside and let Quinn appoint him perhaps rather than go to the Senate and be shunned/denied committee slots). The Senate does have the nuclear option after Burris is forcibly seated however - a 2/3rds vote to expel him.
How many votes does it take to stop a senator from taking his/her seat?