Its fun to watch Harry Reid and Barack Obama act all indignant about the political cesspool in Chicago that gave rise to Obama's political career. They're trying everything they can to keep a Blagojevich appointee from taking a senate seat, but their hands are pretty much tied, constitutionally. The senate is allowed to set the "qualifications" of it's members, but not on a case-by-case basis. Article I section 5 covers this:
Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members, and a Majority of each shall constitute a Quorum to do Business; but a smaller Number may adjourn from day to day, and may be authorized to compel the Attendance of absent Members, in such Manner, and under such Penalties as each House may provide.
Each House shall keep a Journal of its Proceedings, and from time to time publish the same, excepting such Parts as may in their Judgment require Secrecy; and the Yeas and Nays of the Members of either House on any question shall, at the Desire of one fifth of those Present, be entered on the Journal.
The Seventeenth Amendment provides for the filling of Senate vacancies:
Passed by Congress May 13, 1912. Ratified April 8, 1913.
Note: Article I, section 3, of the Constitution was modified by the 17th amendment.
The Senate of the United States shall be composed of two Senators from each State, elected by the people thereof, for six years; and each Senator shall have one vote. The electors in each State shall have the qualifications requisite for electors of the most numerous branch of the State legislatures.
When vacancies happen in the representation of any State in the Senate, the executive authority of such State shall issue writs of election to fill such vacancies: Provided, That the legislature of any State may empower the executive thereof to make temporary appointments until the people fill the vacancies by election as the legislature may direct.
This amendment shall not be so construed as to affect the election or term of any Senator chosen before it becomes valid as part of the Constitution.
Once again, the Constitution gets in the way of the political comfort of the Democratic Party. Let's just see which is judged more important.