Just got back from a great 2 week stay on the 19th. I rented from Thrifty and booked thru AAA New York.
A major headache was they have a sign saying "American Express Cards Temporarily not accepted. A person working there told me and the others on line the policy had been in effect since October 2015. I only carry Amex and was "lucky" enough to have my wife with me with a Via card or we would have been out of luck, as was the couple in front of me on line.
Generally speaking all we had to do was go to another rental agency. For me that would have been a problem as we had a group of 7 people and I was renting a passenger van. Not the easiest vehicle to find on short notice.