I am doing an amended return and on my state taxes it is asking for a date of payment.
Contact Support.
https://ttlc.intuit.com/community/using-turbotax/help/what-is-the-turbotax-phone-number/00/25632
If you are using TurboTax Live, connect with your Live expert.
https://ttlc.intuit.com/turbotax-support/en-us/help-article/product-setup/connect-tax-expert-turbotax-live/L73wOZD5D_US_en_US?uid=l5h7kpw0
If you have a balance due on the state return the program wants to know when you will pay it to compute any possible penalties. Just enter today's date if allowed even if you will not pay it.