They wont have any real problems. They have the Mayor and Governer behind the NYC expansion. The big increase in flights out of LGA will allow them to shift some JFK flying to LGA to help build a new terminal. The design is complete and looks great. The big question is timing and how the port authority will finance everything. Terminals are joint projects since the Port authority retains ownership. Once the new terminal is done Delta plans a major expansion in JFK. Timeline however to complete a new terminal is 4 to 5 years out. There is still some hope for terminal 8 and the Port authority may be putting some pressure on American. That is the first choice. The new design is plan 2.
If they go with plan 2 terminal 3 will be demolished and that area will become a big pad and alley area. No new terminal will be built there. Terminal 4 will be extended almost out to T-way A. Terminal 2 would then be rebuilt after 4 is complete.