It does appear that some New Jersey state tax forms are available but several are still pending. You can check the status of the specific forms needed for your New Jersey return in the link below.
State forms availability table for TurboTax individual (personal) tax products
The 1040 NJ forms are supposed to be available pages 1 thru 4. I still cannot print my return. Please Help . Thanks So Much
Several New Jersey Forms are still pending for printing purposes. Please continue to check back to print your return.
Your table says a basic NJ return only needing pages 1-4 is available, however the program doesn't allow printing of the basic return. So, either your table is incorrect or there is a bug in your software.
TurboTax will not let you print the New Jersey return until all your forms have been approved and available @dmaluchnik.
If you are unable to print your return, it means some of your forms are not ready.
New Jersey will not accept tax returns containing draft or DO NOT FILE copies if you mail those in, even if the numbers are correct.