By invoking race, Rush, who is black, drove a potential wedge between the prospective white and black contenders for the seat. Rush said it would be a "national disgrace" if Obama's seat were not filled by an African American.
Illinois isn't the only state with a seat to fill. As Barack Obama takes over the White House, he leaves in his wake a host of vacancies, and some are becoming the focal points for fresh political battles.
The Illinois governor has said he plans to name the replacement by the end of the year. That person would serve out the remaining two years of Obama's term.
"We don't want (Blagojevich) to short-circuit the will and the wisdom of the state of Illinois," Rush told FOXNews.com, after holding a press conference in Chicago announcing his petition drive for the governor to name a black candidate.
"As we speak, there are no African Americans in the Senate. (Blagojevich) has the power to put one there."
Obama's seat has been occupied twice by a black politician since the early '90s. Carol Moseley Braun, the first and only black woman to serve in the U.S. Senate, held the seat from 1993 to 1999, when Peter Fitzgerald defeated her. Obama then succeeded Fitzgerald in 2005 and served until he resigned last month to prepare for the presidency.
Rush, a former Black Panther member who defeated Obama in a 2000 race for a seat in the House of Representatives, said that he wasn't backing any particular candidate to replace Obama and that he had no insight into whether Blagojevich was leaning toward a white candidate over a black candidate, or vice-versa.
But Rush said, "We don't want to risk being silent in this process." He said he plans to deliver his petition to the governor by Christmas.
Among the potential black candidates who could replace Obama are Rep. Danny Davis, Rep. Jesse Jackson Jr. and Illinois Senate President Emil Jones. Among the other potential candidates are Rep. Jan Schakowsky and Illinois Attorney General Lisa Madigan. Tammy Duckworth, who is Asian-American, also is in the mix. However, speculation is growing that Duckworth, head of the Illinois Department of Veterans' Affairs, will get the nod to lead the national department under Obama.
Chicago political consultant Philip Molfese said Blagojevich has no choice but to consider race in his decision.
"That's, I think, an important consideration the governor has to take," he said. "Barack Obama was the only African American in the U.S. Senate."
Blagojevich's office did not return a request for comment on Rush's petition. However, the Chicago Sun-Times reported last week that Blagojevich may have slipped when he referred to Davis twice last week as "Senator Davis."
Though the governor corrected himself and said he hasn't made his choice yet, he still talked up Davis as a "strong candidate" for the job.
"That's certainly telling of something," said Molfese, president of Grainger Terry. He said Davis and Duckworth are creating the most buzz in Chicago as potential replacements.
Obama's official announcement Monday that Hillary Clinton will be his secretary of state nominee also leaves a vacancy in the New York Senate seat that she holds.
Her departure means New York Gov. David Paterson will have a month or more to choose Clinton's successor. The window could lead to a frenetic holiday season in New York politics. Among those mentioned as potential successors are New York Attorney General Andrew Cuomo, Buffalo Mayor Byron Brown and a number of representatives in Congress.
Rep. Nita Lowey, one of the more prominent potential replacements, told The Associated Press she is not interested in Clinton's seat. But other potential candidates from the halls of Congress include Reps. Kirsten Gillibrand and Brian Higgins, both of whom would satisfy those seeking someone from upstate New York. New York City contenders include Reps. Carolyn Maloney, Jerrold Nadler and Nydia Velazquez.
The replacement process for other Cabinet selections is a bit more clean-cut.
New Mexico Gov. Bill Richardson is expected to be named as Obama's commerce secretary on Wednesday. According to state law, the former presidential candidate would be replaced in New Mexico by Lt. Gov. Diane Denish. She would then have to run for re-election in 2010.
"It's automatic in our state," said James Flores, spokesman for the New Mexico secretary of state's office. "As soon as (Richardson's) gone, our lieutenant governor will move up to the governorship at that time."
Arizona Gov. Janet Napolitano was nominated by Obama on Monday to be his Homeland Security secretary. The move means the Arizona Democrat will be replaced by a Republican, Arizona Secretary of State Jan Brewer. Brewer is a veteran Republican officeholder with more than two decades as a legislator, county supervisor and secretary of state. Arizona does not have a lieutenant governor.
Vice President-elect Joe Biden already has his replacement in the U.S. Senate. His former aide, Edward Kaufman, was named late last month by Delaware Gov. Ruth Ann Minner to fill the seat. Kaufman plans to serve until the 2010 election, and said he is comfortable stepping down at that point.
Speculation had centered on Biden's son, Delaware Attorney General Beau Biden, but the Delaware official announced last month that he planned to fulfill his National Guard duties and would not accept an appointment. Biden is a prosecutor for the 261st Signal Brigade, which left for Iraq in November. Beau Biden could, however, run in 2010.
The Associated Press contributed to this report.