Update: After finding the IRS date on the filing instructions page for when my payment would be withdrawn from my bank account (April 14) but not finding it for the State date, I assumed (silly me) that the State funds would be withdrawn on the same date, and planned to have money in the account to cover both.
Randomly, on April 10, the State funds were withdrawn, with no warning. Luckily, I had enough money available to cover the money due, but wow, this is randomly bad.
I think next year I'll try some other product.
