I wouldn't recommend it. If you've already filed your return and chosen to use direct debit for your state taxes on a specific date, you could create more confusion for yourself by paying the state before then. It's likely that the state would take both payments, and you'd have to straighten out that mistake.
If you haven't filed yet, go back through the File section, and when you get to your state balance due, on the screen Schedule your payment change the payment date.
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