Edited after original post:

I'll report this issue to TurboTax Moderators for investigation.

But here's the deal:  You won't be able to e-file your state or city returns until your federal return has been accepted by the IRS.  This is a security measure put in place a couple of years ago.

So I'd recommend waiting until your federal return is accepted, then try to e-file your state return.  See the TurboTax FAQ I'm linking below for instructions on filing your state return after e-filing your state return.

How do I e-file my state after I already filed my federal? 

I have the exact same problem. I just spent about an hour with a specialist. She tried really hard but neither her or her supervisor could fix the problem. I also don't want to file by paper. Maybe they should look into the logic on the form and fix the date parameters to the four digit year. It is Y2K all over again.

Let's first try clearing your browser's cache and cookies or using a different browser to see if this allows you to proceed with editing the form and e-filing.

If the above doesn't work, try again to delete the city form using the steps listed in this Help Article:  How do I view and delete forms in TurboTax Online?  Then, re-add the form and proceed with e-filing.

Are you still having this issue? If so I would like to research this further for you by getting a Diagnostic Copy of your return.  This will give you a Token Number that you can safely share with me here.  No personal info will be shared with us on this copy; only numbers.  

Here are the instructions

1. Go to TurboTax Online. 
2. In the left side bar, select Tax Tools> Tools.
3. In the pop-up window Tool Center, choose Share my file with Agent.
4. Select Ok on the pop-up and you will get another pop-up with a Token Number 

Thanks!