I use Expedia to book hotels around FRA, even though I stay at the same place all the time. You will find some good deals this way and it is easy to comparison shop. Even close in to the date needed there are a number of Expedia deals.

NH Rhein-Main in Raunheim is quite often very cheap at about 50 euro.
Post Hotel in Sindlingen is reasonable
Both of these hotels have free shuttle service (many more also have a free shuttle) and are in small towns.

Since this is January 2007 and a Saturday night, you have lots of time to wait for something to come along.