Brady said he would not be surprised if 40 people approached him eventually, hoping to get party backing for Green's $125,207-a-year Council seat.
"I'll be left with one ingrate and 39 people mad at me," Brady said.
Council vacancies are filled by special election, with candidates chosen by party leaders, not voters in a primary.
Green will not have to quit his Council-at-large seat until the state Senate confirms his nomination to the school post. Council President Darrell L. Clarke, who would schedule the special election, told reporters Friday that there was no point in discussing the timing of a replacement until Green actually resigns.
Nevertheless, speculation has begun, not only about who might fill the expected vacancy but how that decision could help Democrats resolve one of their looming primary battles over seats in the legislature.
One is the Northeast Philadelphia battle between State Reps. John Sabatina Jr. and Ed Neilsen, since Neilsen's district was erased by redistricting. Another is 23d Ward leader Danny Savage's bid to unseat State Sen. Tina Tartaglione.
Either dispute would dissolve if one of the candidates were willing to give up the legislative race in return for a Council seat. But that at-large position would last only through 2015, when Green's term ends. His successor would have to best a crowded, citywide field of Democrats and Republicans to win reelection.
Making peace among the city's Democrats, their leader said, is easier said than done. "I'm inclined to stop fights anywhere I can," Brady said Monday. "It would be nice, but I'm not sure we can make it happen."
More predictable is the impact of Green's exit on Council's dynamics: not much, considering the body's current aversion to difficult, narrow votes. Most bills pass unanimously. Even Mayor Nutter's property tax overhaul - the most contentious measure of the last two years - passed on a 12-4 vote.
Bills rarely face a final vote with an uncertain outcome in which one member could turn the tide. Close votes have become even rarer under Clarke, who has worked behind the scenes to craft solid majorities.
Green has been one of Council's few iconoclasts, willing to cast protest votes. The last two years, he voted against the city's operating budget, casting the lone dissent in 2012.
With Democrats outnumbering Republicans by 14-3 on Council, his absence would hardly hurt his party. Like the city itself, Council traditionally has divided along lines of political alliances, neighborhood, race, and class rather than party, and even those divisions have faded somewhat amid Clarke's consensus-building.
A reliable vote for business and development, Green made a priority of restructuring business taxes.
He was a noted foil to Nutter in his first term, winning a lawsuit to stop the administration's plans to close libraries at the height of the recession.
In recent years, Green has toned down his anti-Nutter rhetoric and worked more quietly toward policy goals, such as a 2011 business tax relief bill, signed by the mayor. Last year, Green criticized municipal unions for shouting down Nutter's budget address, calling the tactic "outrageous."
Another Democratic power, John J. "Johnny Doc" Dougherty, a ward leader and head of International Brotherhood of Electrical Workers Local 98, said that labor, as well as voters in the river wards, had been key to Green's career, and that "I would like to see someone who kind of mirrors the interests he had."
Dougherty called Green "a deep thinker" and said the school post might serve as a political stepping-stone. "If he's successful in this," Dougherty said, "he can pick any job or any office he wants."