Key Illinois Democratic legislators are circulating a letter urging support for the impeachment of Gov. Rod Blagojevich, who was arrested this week on federal corruption charges relating in part to the selection of President-elect Barack Obama’s successor as a U.S. senator.

State Rep. John Fritchey, head of the House Civil Judiciary Committee, sent out the letter Thursday asking Democratic colleagues to say by Friday whether they support a move for impeachment and would like to be added as a co-sponsor of legislation.

“Faced with a significant budget shortfall, a national recession, and a vacant United States Senate seat, we cannot afford to allow Illinois to operate without effective leadership in the (Illinois) executive branch,” said the letter, also signed by Reps. Thomas Holbrook, David Miller and James Brosnahan. “Simply put, it is imperative to replace Governor Blagojevich as soon as is practicable.”

We know Blagojevich isn’t going to fill the Senate vacancy. It’s a question of whether the governor is replaced and Lt. Gov. Pat Quinn (D) picks the next senator, or the state legislature approves a new law calling for a special election.

Now, Greg Sargent makes a good point — if an impeachment drive gains steam, it suggests the support for a special election may be waning, and state lawmakers are content to let Quinn step up and take the lead. Greg noted, “This would force many legislators, and Quinn himself, into the awkward position of backing an appointment after having declared support for a special election, but it could also mean the seat gets filled much faster, putting the mess behind everyone.”

Quite right. I’d add that it’ll also be interesting to see what steps, if any, Blagojevich takes to signal his support for a special-elections bill. He has to know he won’t be able to fill the vacancy, but if Blagojevich can cede his vacancy-filling authority and hold onto his position for a while longer, that’s obviously a deal he’d take in a heartbeat. Does he dare start signaling to state lawmakers his willingness to sign special-elections legislation?

For that matter, if lawmakers realize that Blagojevich desperately wants there to be a special election, do they avoid that route, just to make sure the governor doesn’t get what he wants? Something to keep an eye on.

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.