It is most likely because your state has not finalized their forms yet. Please see the FAQ below which shows the date each state is expected to finalize their forms. You'll need to return to the program and file your state return once your forms are complete. https://ttlc.intuit.com/replies/3319879
The link you provided says the NJ 1040 form is available. But still the Home & Biz program won't let me open it up and fill it out. I don't see it in my list of forms either.
Are you using TurboTax Online or TurboTax CD/Download? If you have TurboTax Online you can clear your cache and delete cookies. Also, try refreshing your browser and even try using a different browser.
Here are two articles below that will show you how to clear your cache and delete cookies.
How to clear your cache - Community
How do I delete cookies? - Community
If you have TurboTax CD/Download, please check for updates within the program.