You should get a refund, or a transfer to another airline.
In my opinion if an airline such as Jet Blue goes bankrupt (chapter 7 - dissolution) they will not do anything for you and they will not have any obligation to do so. If they go chapter 7 they may have little or no staff left to do anything on your behalf or for any of their customers.
The major airlines like Delta and American have never liked Jet Blue and unless there is something in it for them they will not do anything to help bail out Jet Blue or its customers. They have enough problems of their own.
If they go chapter 11 (reorganization) you have a prayer but chapter 11 is highly unlikely.
In this business climate chapter 7 is more likely given the failure of the fools in congress to tell the world that they would allow vigorous drilling for new oil reserves in the US thereby immediately cutting the oil price speculators off at the knees and reversing the upward trend in oil prices. Good grief, one idiot California congresswoman even spoke today about the possibility of congress nationalizing US the oil companies. That was not helpful!!
The US airline business model is not based on $150/barrel oil. Low margin operators like Jet Blue cannot sustain their business operations in this environment.
If I were you I would absolutely use the ticket as soon as possible. Tomorrow would be good.
Good luck and 73 from the Fisherman.
Yes, JetBlue will find other airlines that serve your route. Just like when ATA and Aloha Airlines went out of business, United Airlines, American Airlines, etc, were all there to assist customers. You may have to pay a little extra money though. Hope I helped!