You're problem is not with really with ASCAP, it is with the venue, who are trying to get you to agree to assume their liability, which would not ordinarily be your own.

The thing is, if there is a question, dealing with it would fall on you, and could end up costing you more money than you stand to make, even if the licensing organization's claim against you turns out not to have merit--

Win or lose, you'll have attorney's fees, say an initial $250 for the initial consultation, and $250-500 per hour after that. Even if it's just a couple phone calls and a letter, the meter can run up pretty fast.