A robo caller was on when I answered, and when I waited a while a human came on. A guy in an Indian accent came on and asked me what my current interest rate was. He said he could do better than that and  asked me for my credit card type and number to get started. I asked him what bank he represents. He didn't answer the question and instead just did some more of his sales doubletalk. When I told him I don't do this type of thing over the phone and would he just mail me something. He hung up at that point.

I have received two other calls with the exact same scenario, although in those cases I didn't record the caller id. I'm sure it's the same place because I remember those calls also came out of New York. But in these two calls they did name a bank, but the two calls I received were using different bank names.

This really reeks of being a scam. Reverse phone look-up only yields that it is a land-line in NYC.
I did report the call to the FCC on-line complaint system at this URL:

http://esupport.fcc.gov/complaints.htm

DON'T give anybody that calls your phone your credit card number!