Seating Burris seemed more likely late Tuesday, when Sen. Dianne Feinstein rejected the reasoning that all of the chamber's Democrats, herself included, had cited in a letter last week - that corruption charges against Burris' patron, Illinois Gov. Rod Blagojevich, tainted his appointment.
"Does the governor have the power, under law, to make the appointment? And the answer is yes," said Feinstein, chairwoman of the Senate Rules Committee, which judges the credentials of senators.
Burris marched into the Capitol earlier Tuesday, declaring himself "the junior senator from the state of Illinois." But Secretary of the Senate Nancy Erickson rejected his certification, as he knew she would, saying it lacked Illinois Secretary of State Jesse White's signature and the state seal.
Late Tuesday, Feinstein urged the Senate to settle the matter.
"If you don't seat Mr. Burris, it has ramifications for gubernatorial appointments all over America," the California senator said. "Mr. Burris is a senior, experienced politician. He has been attorney general, he has been controller, and he is very well-respected. I am hopeful that this will be settled."
A spokesman for Senate Majority Leader Harry Reid did not immediately respond to a request for comment.
Earlier, Reid had said, "Mr. Burris is not in possession of the necessary credentials from the state of Illinois."
Burris, meanwhile, pivoted from his rejection at the Capitol to the Illinois Supreme Court, asking it to order White to certify his appointment.
Burris was expected to meet with Reid on Wednesday.
It would be his second appearance at the Capitol in as many days. His first included an escort by Capitol police officers to Erickson's third-floor office for what was described as a highly cordial, 21-minute meeting.
Burris, 71, then led a small mob of lawyers, consultants, police and reporters across the street in pouring rain, to a news conference which Burris aides said Reid had tacitly allowed.
Erickson, Burris reported, had advised him that "I would not be accepted, and I will not be seated, and I will not be permitted on the floor."
The former Illinois attorney general said he was "not seeking to have any type of confrontation" over taking the seat. In addition to his court filing late in the day in Illinois, Burris said he was considering a federal lawsuit to force Senate Democrats to seat him.
It was a distraction for majority Democrats eager to project an image of progress with Obama on an economic stimulus package estimated to cost as much as $800 billion.
Democrats and Obama have said that the corruption charges against Blagojevich would strip credibility from anyone he appointed to the seat.
Blagojevich denies federal accusations that he tried to sell the seat Obama has given up for the presidency.
In a written statement Tuesday, the governor said allegations against him shouldn't be held against Burris, whom he called a "good and decent man."
"The people of Illinois are entitled to be represented by two senators in the United States Senate," Blagojevich said.
An attorney for Burris, Timothy W. Wright III, said that "our credentials were rejected by the secretary of the Senate. We were not allowed to be placed in the record book. We were not allowed to proceed to the floor for purposes of taking oath. All of which we think was improperly done and is against the law of this land."
Some of Burris' supporters have bemoaned the fact that Democrats would stand in the way of the Senate gaining its only black member. Burris himself downplayed the issue of race, telling reporters: "I cannot control my supporters. I have never in my life, in all my years of being elected to office, thought anything about race."
"I'm presenting myself as the legally appointed senator from the state of Illinois. It is my hope and prayer that they recognize that the appointment is legal," he said on CBS' "The Early Show."
Members of the Congressional Black Caucus said Tuesday that Burris should be seated.
"A lot of people want to talk about race or the governor and his problems, but the bottom line is you have a sitting governor who has certain legal rights and authorities and he's made an appointment," said Rep. Elijah Cummings, D-Md. "This is an issue that goes beyond race."