On November 21, Congressman Jesse Jackson, Jr., resigned, only 15 days after he had been re-elected from the Illinois 2nd district in Chicago. See this story, which says that under Illinois law, taxpayers will spend $5,000,000 administering a special primary and a special election. The law requires the special election no later than March 21.
The November 6 election had three candidates on the ballot. Besides Jackson, there was a Republican and an independent, Marcus Lewis. The story linked above says Lewis plans to run in the special election. Assuming he wants to run as an independent in the special election, he will need a petition signed by 5% of the vote cast in the November 2012 election. That will be at least 14,336 valid signatures, a very severe burden. He only needed 5,000 valid signatures to qualify for the November 2012 election, because the 5% formula is not in effect for U.S. House elections in the year after redistricting.