Even today's date?

Yes, even today's date.  I've tried using dates in the future - dates in the past - today's date.  It doesn't matter.  The federal return works just fine.  Only Virginia is not working. 

What does the error message say?

Philadelphia Net profits has the same problem. No date works for debiting.

I believe you can make the payment directly on VA's website. This is from VA's form 770 instructions:

 Use the Department’s website, www.tax.virginia.gov,
to make a payment online. Payments are electronically
transferred from your savings or checking account. There is
no fee charged by the Department

Once you get past the original due date (7/15/20, or 4/15 every other year), PS federal does not allow entering a future date, probably because the tax was already due and you will just be later. YOU MUST ENTER "TODAY'S" DATE FOR FEDERAL.

The same is true for NJ and PA, but not for Philadelphia(and apparently VA). Phila gives you the error that it cannot be later than the due date(7/15) but it also won't accept any other date.

"Payment date must be equal to current date if filing due date has passed." I tried to use 7/15 today.

"Payment date must be between 1/1/20 and 7/15/20" when trying to put in Today's Date.

For federal and for some states, if you don't want to pay today, then you have to hold off on e-filing and e-file only on the exact date you want to debit. So if I want to pay on 10/1/20, I have to wait to e-file on 10/1/20.