Even if the seat tube length of a 20" bike will work for you, the length of the top tube on that size frame might make the bike pretty uncomfortable if you have to lean forward a lot to reach the bars.

If you're willing to make the drive SE a bit (and enter Wolverine territory ), there's always a ton of pretty decent, inexpensive used bikes in Ann Arbor on annarbor.craigslist.org

Good luck!