According to this story, when Speaker John Boehner resigns, election officials in Butler County, Ohio, will be required to spend approximately $1,000,000 for a special primary and then a special general election to fill his seat. Boehner hasn’t actually resigned yet so the Governor hasn’t yet set the date of a special election. It seems conceivable Boehner may change his mind and not resign, although the article doesn’t discuss that. Butler County is one of six counties in the Eighth District, so presumably the total election administration of the special primary and special election will be perhaps $5,000,000.

The article quotes Butler County Commissioner Don Dixon as saying that Congress should just appoint a temporary member of Congress, but Article One of the U.S. Constitution does not permit anyone to serve in the House who had not been elected by the voters.