UPDATE: Thank you so much for all of the great advice! We obviously decided not to accept this position and we're taking our time and searching for other options.

Just to set the record straight, we don't feel that we were acting desperate by considering this position. We've been looking for over a month and we've had a challenging time finding a quality school that'll accept all four of us because there's one person in our group without a degree or TEFL. We'll just have to look harder! This is our fourth **** job that we'll be turning down.

Thanks again!!