How do I change the withdrawal date for my state return that I filed through turbotax? I owe over $300 in state taxes and would prefer to stagger the payments.

You will have to contact your state to cancel the payment and then make arrangements to pay in installments.

See this TurboTax support FAQ for contacting the Department of Revenue by state - https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-revenue/L9qVToi02_US_en_US?uid=lgweq5q3

If you already transmitted your return in TurboTax, there is no way to change any part of the return with TurboTax, including payment dates.