Well, maybe you could let your users answer that one for you by putting an SDK page up with 'coming soon - email us for a beta test' and tracking hits/emails. You'll probably change so much after launch that you don't want to be stuck trying to support API 1.0 so unless you get a lot of requests for it , it's probably a bad idea.
I agree with the others that you shouldn't focus on an API for rev 1.0 in order to get the product to market. But I would be careful and architect the code such that it can support an API...otherwise it's going to be a real pain in the rear to retrofit.
Depends on your target audience. What do your users want? If you don't know, ask them -- not us! (And if you don't have any idea who your target users are, you have a bigger problem than the API...)