I am not exactly sure but I just had one on friday and was 19 weeks. I was debating if I wanted to get one now or wait until the blood work was in and then go from there. The blood work takes 2 weeks and my high risk doc said no hurry. So you are probably still fine. Good luck!
I think it's actually 24 weeks, lol I was remembering after I posted, so i'd definately call tomorrow and tell them, they will get you in for it faster since your 23 weeks.
Technically they can do it anytime but there is a time when it becomes less reliable and i dont remember the cut off. I'd definitely ask your doctor.
I believe they can do it anytime, but i'd call your doctor tomorrow and tell them you want to do it. They will get it scheduled asap. =) Good Luck!