Be careful about this question for a few reasons. First of all, it doesn't mean you "got the job." They may be just checking to add that to their notes. You must keep your guard up until you are in your car and driving away from the interview.

If you are currently employed, you should be honest about the start date and show professionalism. You should tell them you would have to discuss a transition with your current company and see if they require a two-week notice. If you currently have a critical role, your potential new employer would expect a transition period.

If you can start right away (and they know you are not currently employed), you certainly can say you're able to start tomorrow. Sense of urgency and excitement about starting work at the new company is always a good thing.