yes, they offer the American DAT everyday except for the weekends. If you already applied, you should be receiving the eligibility letter (email) with your eligibility number in it. Note that this is different from your application number. I got the eligibility letter three days later. With that number you can log on to the prometric website (www.prometric.com), and you can choose whatever date you want. BTW, from what I remember, it was all booked up until June in my area, but some people make the last minute changes, so you can always reschedule as soon as you see an opening (US$20 or $25 for rescheduling).
I had planned on taking mine around May 20-25, and luckily I was able to get mine registered on Sat. the 23rd. So in my instance I was able to get a time that was suitable to me. I wish you luck on getting a date.
