I don't think they would fly JFK-SWF. Perhaps they would start service to Florida or West Coast.
Carnival offered non stops to Florida from there in the early to mid 90's, so it's not unheard of.
I'm not sure if jetBlue would want to compete with itself on its JFK routes, but if there is some kind of incentive being offered at SWF, then it could be possible.
this might also be a solution for jetBlue on what to do with its planes that will be arriving the near future. I think I heard on here that they are arriving one every other month. They are adding a 3rd Long Beach-JFK roundtrip and adding seasonal flights to Florida so this should keep them busy for a little while. I've been curious what they will do after the attacks and if they will delay delivery on some of their planes. So, this could occupy their planes if they don't want to deploy them at JFK
Personally I'd be really excited if they started flying there, SWF is so much closer to my house than JFK and I love flying jetBlue.