You should be good to go. 
You're all good.
My only advice is to make sure the clinic/office accepts AMEX.
Went to the theater last week, handed the card to the clerk to pay for snacks; made a joke & quoted the old VISA slogan: "And they don't take American Express"
To my great surprise he said "that's right, we don't" Eeeks.. My funny went sour.. I had many alternate cards but I was a little shocked..
CHEERS and Good Luck for a speedy recover from the procedure!!
@Anonymous wrote:Friends,
This month I got an Amex Everyday Card. My Credit Limit is $5,000
On Tuesday, I'm having LASIK and it costs $3661.80.
Amex says (via their online live chat) that this charge will be approved.
I plan to pay the card in full on the same day (I have cash in the bank for the procedure).
I still feel a bit squeamish about it being approved (even with their reassurance), should I bring cash just in case?
Thoughts?
P
You should be good to go. Just as a bit of advice, the "check purchasing power" also works, so you don't have to chat in with a rep. 
Your ED card is on a 0% APR for a while, correct?
If you are in your first month with AMEX, you may be limited in how many payments you can make.
But you at least have a grace period, and you won’t be able to pay in full on that day; the charge will be Pending for a few days.
I would relax for a few days, enjoy the LASIK results, and then after it prints on the upcoming statement, pay in full ahead of the payment due date after that statement. This is to allow a large balance to print in your credit history so that other banks also see you can make large charges and pay them off. Utilization will go up temporarily, yes, but you will have a large balance in your file for years to come.
