For Texas residents, federal taxes owed on a 2020 tax return have to be paid or on before June 15, 2021 to avoid a failure to pay penalty.
IRS website - https://www.irs.gov/newsroom/irs-announces-tax-relief-for-texas-severe-winter-storm-victims
As a result of the winter storm, Texans have until June 15, 2021, to file various individual and business tax returns and make tax payments.
For additional information, see the IRS article: Victims of Texas winter storms get deadline extensions and other tax relief.
Yes, TurboTax recognizes this extended deadline for Texas residents, but if you plan to send your payment after May 17, 2021, you will have to either mail a check or pay on the IRS website as you will not be able to schedule a direct debit through TurboTax after May 17.
For more information, there is a link on the bottom of the "How Would You Like to Pay Your Taxes?" screen in TurboTax Online. See sample screenshot below.