Reid spokesman Jim Manley, by way of Ben Smith, has word on the Majority Leader's potential workaround:
In response to those who are asking how this is different from Powell v. McCormack, in which supreme court said House could not refuse to seat a member based on his alleged corruption and said only qualifications to be considered are those listed in the Constitution:This is certainly a stronger argument than trying to challenge Burris's qualifications, something which was explicitly addressed by McCormack.
[W]e are not making a judgment about qualifications of appointee, but about whether appointment itself is tainted by fraud, which we believe we are entitled to do under Art. 1 s. 5.
This is like judging the integrity of an election, free from fraud or corruption. It's the process that led to the [appointment], not the appointee's fitness.
Article 1, Section 5 of the Constitution holds that "Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members". If Reid is not attempting to judge Burris' qualifications, then he'd presumably have to argue that a Senatorial appointment is tantamount to an "election", which seems on the surface like a liberal reading of that term. EDIT: Some of the lawyers in the comments section, however, seem to think that this is a trivial distinction, and cite previous instances (.PDF) in which the Senate did attempt to challenge an appointment.
Nevertheless, if you read the McCormack opinion, the principal reason why the Court decided to interpret the qualifications clause narrowly is because there is an alternate mechanism available to the Senate: expulsion. The Court conceivably might hold that the other provisions of Art. 1 s. 5 should be interpreted narrowly for the same reason.
We should keep in mind, however, that ultimately winning this court case doesn't necessarily do a whole lot of good for Reid. All that would mean is that the Democrats would be short a senator until Illinois either held a special election or impeached Blagojevich, neither of which appear likely to happen especially quickly. Rather, the goal is to find some pretense by which the Democrats can keep Blagojevich at arm's-length -- and forcing Burris to go to court to get his seat would presumably allow them to do that.
NOTE: Edited for truthiness.