There is often a lag between acceptance for federal and state. The state cannot be accepted until the IRS has accepted federal . And there has been a very high volume of "filing" going on. Give it a little more time.
When you e-file your federal return you will receive two emails from TurboTax. The first one will say that your return was submitted. The second email will tell you if your federal return was accepted or rejected. If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.
New Jersey is a bit slow. It usually takes 2 to 3 days after your federal return is accepted to get the acceptance from New Jersey. It might take even longer at this very busy time.
It's not unusual for state returns to remain in pending status several days after a federal return has been accepted. It's common for this to happen as we approach tax day.
Please see the TurboTax article Why is my state e-file still pending?