When Rich Daley shocked Chicago on Tuesday by announcing that he would not seek reelection to a seventh term, speculation about his potential replacement heated to a boil — everyone from White House Chief of Staff Rahm Emanuel to Rep. Jesse Jackson Jr. (D) to the Cook County sheriff to the Cook County assessor to a dozen aldermen whose names were obscure even to the political junkies among us.

As Tuesday wore on, the list of possibilities lengthened so quickly, I was surprised not to see on it the political basket case also known as Roland Burris (D), Illinois’s junior senator. (He’s the endless embarrassment whom disgraced Gov. Rod Blagojevich, D, named in the short period between his arrest and impeachment to replace Obama in the U.S. Senate; it was Blago’s way of saying, “Screw you” to the state’s establishment.)

Not surprisingly, given the Daley family’s dynastic tendencies, the mayor’s brother, Bill, his son, Patrick, and his nephew, Peter, also made the list.

Rich Daley also has two daughters; no one mentioned them, or any of his nieces. Women were definitely not in the mix.

The few females whose names surfaced carry so much baggage that their road to the Feb. 22, 2011, election and the inevitable April 5 runoff would prove difficult to impossible.

— Attorney General Lisa Madigan? Her father, Michael Madigan, Speaker of the Illinois House, is, hands down, the most powerful player in the state, and he has so many conflicts of interest that Lisa, who seems to want to be governor anyway, would watch her credibility and future shredded in a mayoral race.

— Alderman Sandi Jackson? The wife of Jesse Jackson Jr., a man who is barely treading water since his name popped up all over the Blagojevich trial, as a man whose backers were allegedly willing to give big bucks to Blago in exchange for his appointing Jackson to the Obama Senate seat. Blago’s retrial starts this January and Triple J, as he is known, will be dragged through the mud again.

— Cook County Circuit Court Clerk Dorothy Brown? Her recent race for Cook County Board president was crippled by reports that she charged employees $2 for the privilege of wearing jeans to work on Fridays. (The money, she said, went to help employees with family problems and to host morale-building employee social events.)

— Presidential senior adviser Valerie Jarrett? Obama’s key adviser and confidante to first lady Michelle ObamaMichelle LeVaughn Robinson ObamaObama plans to use Netflix deal to stop political divisiveness Michelle Obama tweets out first look at cover of new book Netflix surpasses Comcast in market value MORE is well-known in Chicago, but considered a failure in one of her key responsibilities — serving as a liaison between the president and the business community. Besides, Michelle wants to keep Valerie close by the White House. Michelle had a role, reportedly, in Jarrett’s not pursuing an appointment to her boss’s old Senate seat.

In the history of Chicago, only one woman has served as mayor: Jane Byrne, from 1979-83. She was a disaster on almost every count, but, hey, we’ve had our share of incompetent male mayors as well.