Talk to them asap...I guess they donot have experience on H1-B sponsorships, and you donot have too much time to waste, it is in the middle of Jul already.

I assume they will contact a immigration lawyer before giving you a response. meanwhile you'd better talk to an experienced lawyer about your case too( see how much your case is qualified..e.g. will the company size be an issue?).

Things can be negotiable, especially for a small company.. I mean If I were you and I really like this job, I will do my homework on H1-B file process and explain detail info to the boss, so he knows what info he is supposed to provide and his responbilities..etc. Then you can sit down and talk..say you would appreciate his help on H1-B and your future good work will pay back...... blahblah..

As I know, being a H1-B sponsor, a company basiclly just need to provide some finicial and background info of the company. 

Also, try the best to let them pay for the fee!