Akhil Reed Amar and Josh Chafetz make it; the entire piece is worth reading, but here is what strikes me as the heart of the argument:

Each house of Congress is "the Judge of the Elections, Returns, and Qualifications of its own members," according to Article 1, Section 5 of the Constitution. At the founding, Senators were elected by state legislatures. If the Senate believed that legislators in a given state had been bribed into voting for a particular candidate, the Senate could refuse to seat him.

Because of the word "returns" in Section 5, what is true of elected Senators is equally true of appointed Senators. According to the Oxford English Dictionary, a "Return" in the time of the framers involved a report of an appointment made by a sheriff or other official.... [T]he Constitution itself sets up the Senate as the highest court of Senate elections. When the Senate speaks as this court, its adjudications are legal judgments that no other court may properly reopen....

To be sure, there is no evidence Burris bribed the governor to get this seat. But imagine if Burris had won election only because other candidates were wrongly and corruptly kept off the ballot. Surely the Senate could properly deem this an invalid election. Similarly, it now seems apparent that there were candidates that Blagojevich refused to consider for improper reasons — because one refused to "pay to play" early on, or because another is at the center of the impending criminal case against the governor. With the appointments process so inherently and irremediably tainted, the Senate may properly decide that nothing good can come from a Blagojevich appointment....

Nor does it matter, from the Senate's point of view, that Blagojevich hasn't yet been convicted. In this context, the Senate itself is a judge, in the words of the Constitution, and can decide facts for itself. It need not follow the rules of criminal courts. That means it need not find Blagojevich guilty beyond reasonable doubt, as a court would if his liberty were in jeopardy. It is enough for the Senate to reject Blagojevich's appointee if a majority of senators are firmly convinced that Blagojevich is corrupt and that any nomination he might make is inherently tainted by such corruption....

I have a very high opinion of Amar and Chafetz, but here I think they're mistaken, and I think Brian Kalt (Concurring Opinions) has it generally right: The initial misconduct on Blagojevich's part doesn't carry over to a bribe-free appointment of the person he ultimately appointed. In any case, though, read Kalt's argument — family duties keep me from blogging further on this myself.

UPDATE: Ann Althouse has more.

FURTHER UPDATE: Michael Rappaport (The Right Coast) likewise disagrees with Amar & Chafetz:

Consider the following analogy. Amar and [Chafetz] write: "At the founding, Senators were elected by state legislatures. If the Senate believed that legislators in a given state had been bribed into voting for a particular candidate, the Senate could refuse to seat him." That is true, but if the same state legislature produced another candidate, without any evidence of bribery, the Senate should not be allowed to refuse to seat him.