the threat didn't work, blago called their bluff and appointed roland burris. there is no real basis for denying burris the senate seat. the illinois governor has the power to appoint, blago is still the illinois governor, and so his pick is legitimate. harry reid can't, and shouldn't, do anything about it.
the problem is that reid is already on record saying that he would not seat a blago appointment. and so he's relying on a technicality to try to deny burris the seat:
The problem for Mr. Burris, of course, is that he was named to the seat by the embattled Illinois governor, Rod R. Blagojevich. Ms. Erickson had already said that the appointment letter forwarded by the governor’s office did not comply with Rule II of the Senate’s standing rules, which requires signatures of both the governor and the secretary of state.this technicality creates a bad precedent. in a lot of (if not all) states the governor and secretary of state are elected on separate tickets. it's quite possible for the two positions to be held by members of different parties. if a senate seat can be denied because the state SoS doesn't sign a piece of paper, the secretary of state has an effective veto over who gets to sit in the senate, or at least a method to temporarily deny the opposing party a senate seat.
The Illinois secretary of state, Jesse White, has refused to sign, saying the appointment is invalid because of the federal corruption investigation surrounding the governor and what prosecutors describe as his efforts to sell the Senate seat, vacated by President-elect Barack Obama.
it's not hard to imagine how this rule can be abused by either party in the future. this is a bad precedent and although it may delay burris' senatorial career, i don't see any way that reid can ultimately deny burris the seat. any utility in the threat to block the seating of a blago-appointed senator expired when blago went ahead and appointed burris. there's no point in engaging in an ultimately losing battle to prevent the burris appointment when the fight itself can create a bad precedent that may ultimately come back to haunt the democratic party in the future.