CHICAGO (CBS) — State Sen. James Meeks on Wednesday called on the his two fellow African-American candidates for mayor to get together to decide which of them has the best chance to win and then have all three back that candidate.

But the surprising suggestion was quickly shot down.

It certainly wasn’t the first effort at picking a consensus African-American candidate to run for mayor.

After Mayor Richard M. Daley announced he wouldn’t seek another term, a group of African-American business and community leaders engaged in a confusing and controversial process to pick a so-called “consensus candidate.”

They ultimately decided to back U.S. Rep. Danny Davis, but that didn’t stop Meeks and former U.S. Sen. and Ambassador Carol Moseley Braun from running too.

On Wednesday, Meeks apparently took another stab at coming up with a consensus candidate.

During an panel discussion WVON Radio, host Cliff Kelley held up a cover story from the Chicago Defender – the historic black newspaper – with the headline “If All Three Run, We Lose.”

Meeks and Braun were in the studio with Kelley, while Davis was on the phone from O’Hare International Airport, when Meeks made the startling offer.

“My hope is that before December the 21st, that the Ambassador, Congressman Davis and myself come together and sit down and have a discussion,” Meeks said. “I am willing to sit down at the table and have a serious conversation with the two of them about what’s at stake.”

It was an offer that Davis seemed to consider, but that Braun immediately rejected.

“The short answer is I’m not dropping out,” Braun said. “I’m in it to win it and I’m in it to the end and … I’m giving no quarter on this.”

Davis said, “I certainly don’t have a problem with that at all. I don’t know anybody who pushes the concept of unity more than I have.”

Davis was picked as the consensus candidate only after the group of business leaders had first narrowed their picks down to Meeks and Board of Review Commissioner Larry Rogers. Not long after, they restarted the process with Meeks, Braun, Davis and Rogers.

Just about the only thing the Meeks, Davis and Braun agreed on Wednesday was the need for equal opportunity, fairness and balanced leadership for all Chicagoans.

Meeks’ trial balloon for all three backing the candidate with the best chance quickly went down in flames.

Earlier in the day, Meeks unveiled his education plan, which included a call for full-day kindergarten citywide, doubling reading and math instruction time in grades 1 through 3 and offering $4,500 school vouchers to 50,000 low-income students to attend any school in the city.

It was another concept Braun immediately rejected.

“The Senator would like to privatize our schools,” Braun said.

But Meeks said “it’s going to take us at least 7 to 10 years before we turn this system around. Why not give 50,000 students and their parents a choice?”

It’s a concept Meeks has pushed in the state legislature before, but his proposals have been shot down. He said he thinks if he’s elected mayor, lawmakers would be more willing to go along with his plan.