No. It is not possible to pay Federal taxes due out of a state refund, nor can one pay state taxes out of a Federal refund. Those are 2 separate tax agencies, and there are over 40 state tax agencies. The IRS wouldn't want to do all that. They want their money upfront.
I'll give you a FAQ below that tells some ways to pay Federal tax due, and following that, I'll tell you about a way to pay it at the IRS website, if you wish.
FAQ: How can I pay my Federal taxes?
If you don't wish to use one of those methods, you can pay any Federal tax due at the IRS Direct Pay website with a free ACH electronic debit of your bank account (there's a service fee if you choose credit/debit card.)
If you intend to go the IRS Direct Pay route, you would tell TurboTax that you are going to pay by "check" so that it lets you finish and file. That doesn't obligate you to pay by check.
Then, if you decide to pay at the IRS Direct Pay website, in the form there at the IRS site you would choose for "Reason" that it's for "Tax Return", then choose to "Apply Payment" to "Form 1040/A/EZ", then indicate the proper tax year (such as 2019 for a current return.)