Balkin describes the issue this way:
Article I, section 5 reads: "Each House shall be the judge of the elections, returns and qualifications of its own members."
Hence the Senate may refuse to seat Burris for three reasons: because he is not qualified under Article I, section 3, because the election returns do not support him, and because his election was not properly conducted. ... Section Two of the Seventeenth Amendment modifies Article I, section 5. It states:
"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."
Thus, you might argue, the Senate must treat a person appropriately appointed by the executive authority of the state as duly elected for purposes of Article I, section 5.
But that is precisely is the basis of the Senate's refusal to seat Burris. In the Senate's view, Burris has not been properly appointed by the executive authority of the State of Illinois.... {because}, for starters, it looks like the Governor might be corrupt and was trying to sell the seat.
But, you might respond, the Governor has not been convicted of anything. Surely he is innocent until proven guilty.
True enough. But Article I, section 5 does not contemplate a criminal proceeding. Rather, it contemplates that the Senate will be the judge of the circumstances of election (or in this case, after the Seventeenth Amendment, an appointment.).
http://balkin.blogspot.com/2008/12/can-senate-refuse-to-seat-ronald-burris.html