Why can I efile my federal tax, but not my State tax. It says I can't efile my NY State tax because of a tax issue, but doesn't tell me what the issue is.

There are a number of 2020 forms  — including the Form 1040 now that the 2nd stimulus passed — that are still being revised by the IRS and the states.  Click on the REVIEW tab to see what form(s) you are waiting for and when it is estimated to be ready (when operational ….and dates are subject to change) ... 

IRS Forms Availability Table for TurboTax Individual (Personal) Tax Products

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State Forms Availability Table for TurboTax Individual (Personal) Tax Products

Although the software will allow you to e-file your federal now, your federal return will just sit in "pending" on the server until the end of January, when the IRS begins to accept/reject 2020 returns.  You gain no advantage by putting your return into pending.  And if you find out you made a mistake, you cannot change it when it is in pending.