It depends on the state you live in and when that state will begin accepting/processing returns.
I am getting the same message("2/3/2020. try back then.") when I try to e-file using TurboTax. For example, Georgia will not begin processing state tax returns until 2/3/2020.
If you're not in Georgia, check with your state's website and see when they will begin processing returns.
It all depends on what state returns you are trying to file as well. Even though the IRS has opened and started accepting e-filed returns, some states have not. You can check the status of when you state forms will be ready for e-filing by clicking here: https://ttlc.intuit.com/community/forms/help/state-forms-availability-table-for-turbotax-individual-.... Once they show available, that means they can be e-filed.
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