If AA is delayed they are required to rebook you on the next available flight. AA has flights to CUN via multiple cities (DFW, CLT, etc) so if you are delayed have them check for connections and not just non-stop options.
If the delay is maintenance and you are forced to stay overnight in NYC, they AA will put you up. If the delay is due to weather, then you are on your own. There is no EU 261 compensation in the US...US airlines don't pay for very much (if anything) anymore. Also, if you are held up in NYC, AA will not pay for any hotel fees, etc you may be charged in CUN for no-showing. So if you are delayed and you know you are stuck in NYC, make sure you call your CUN hotel ASAP to adjust your details accordingly to avoid any no show fees and loss of reservations.