Jesse Jackson Jr.'s resignation from the House could cost Illinois taxpayers more than $5.1 million, according to the state elections board.

Jackson, Jr. offered his resignation today to House Speaker John Boehner, R-Ohio. Jackson has been absent from the Capitol for months while undergoing treatment for bipolar disorder at the Mayo Clinic. In addition, his use of campaign funds is being investigated by federal authorities.

Looking at two special House elections held in Illinois in recent years - those to replace GOP House speaker Denny Hastert and Democratic congressman Rahm Emanuel - the Illinois State Board of Elections calculated those elections cost $2,700 to $4,000 per precinct. With 590 precincts in Jackson's 2nd Congressional District, an election would probably cost around $2,575,000, the state board told ABC News.

Illinois will hold two special elections to replace Jackson, a primary and a general, and the state board projects that replacing Jackson could cost $5.15 million total.

That's just a projection, and it assumes that the 2nd Congressional District will hold the special elections on their own days. State law will likely allow for the primary, but not the general, to be held alongside already-scheduled votes for state and local offices.

Jackson hasn't officially won re-election yet, as the state won't certify election results until Dec. 2. Officials are unsure of whether that will affect how Gov. Pat Quinn handles Jackson's resignation, an official with the state elections board said. Jackson handily defeated Republican lawyer Brian Woodworth with 63 percent of the vote, according to the still-unofficial results.

Quinn, a Democrat, must set a special-election date within five days, under Illinois law. The election must be held in the 115 days after that.

Jackson may have cost taxpayers extra by resigning so suddenly.

To save money, the 2nd District could hold its special election on Illinois' consolidated election schedule at the same time as lesser races throughout the state.

But that doesn't seem possible under Illinois's statutory special-election timeline. Illinois primaries will happen Feb. 26, but the April 9 general-election date falls outside the 115-day special-election range. Counting Thursday as day 1, March 21 is the earliest the 2nd District special election could be held.

Had Jackson waited until Dec. 15 to resign, Quinn could have scheduled the general special election for April 9, along with Illinois' other general elections.

The cost of the special elections will be borne by the counties in Jackson's district, as well as by the state.

Holding a statewide special election to replace governor Rod Blagojevich cost the state between $90 million and $100 million, according to estimates, the state elections board said.