"President-elect Obama agreed with us that Mr. Burris is tainted, not as a result of anything that he's done wrong," Reid said on NBC's "Meet the Press" Sunday. "There's -- I don't know a thing wrong with Mr. Burris. It's not the person that has been appointed; it's the appointee. ... There is a cloud over Blagojevich, and at this stage, a cloud over the state of Illinois. ... And if, as long as Blagojevich has done the appointing, it's really a tainted appointment."
After being booted from the Senate Tuesday, Burris, who dubbed himself the "the junior senator from the state of Illinois," said at a news conference that he is "not seeking to have any type of confrontation."
His attorney, Tim Wright, added that Burris' rejection was improper and "against the law of the land." He said that one option would be to file in the District Court, but that it was up to Burris to decide.
"The state of Illinois has been illegally disenfranchised and denied full representation in the United States Senate when earlier today senator appointee Roland Burris, D-Ill., was prevented from being sworn in to his legally appointed position by the United States secretary of the Senate clerk and sergeant of arms," read a statement from the Burris team.
Burris got a boost from at least one Democrat Tuesday. Senate Rules Committee chairwoman Dianne Feinstein, D-Calif., indicated that she believes Blagojevich still has the power to appoint Burris and that the Senate should respect that appointment.
"Gray Davis was able to be recalled as governor and still make gubernatorial appointments, so as long as you have the power, the power exists," said Feinstein, who is a potential California governor candidate.
Feinstein, who is the incoming chairwoman of the Senate's Select Committee on Intelligence, also grabbed headlines Tuesday for expressing displeasure that she was not consulted by Obama's transition team on Leon Panetta's possible appointment for CIA director.
As the Blagojevich investigation continues, it is unclear whether senators have the right to reject Burris. Election law attorneys have said that senators may not have the constitutional power to refuse to admit Burris into the Senate without some indication that his appointment was corrupt.
The Burris drama is also complicated because it touches on the politics of race. In an almost all-white U.S. Senate, the image of a black politician being banned from the Senate floor injects a new twist to the scandal over Obama's seat.
Burris will return to Chicago after his meeting with Reid and Durbin, and will appear before the Illinois House Special Investigative Committee Thursday afternoon to testify about Blagojevich.
ABC News' Matt Jaffe contributed to the report.