No, you cannot pay Federal taxes due out of a state refund.
Are you sure you're not looking at a "net figure" that combines the Federal and State final figures? TurboTax has a summary figure at the Tax Home that confuses folks because of that summary figure that includes both the Federal and State situations. i.e., if that's what you are looking at, on the Tax Home TurboTax is showing what someone has left in their pocket (the "net") when considering both the Federal and State. That does not mean the Federal tax is being paid out of the state refund, which cannot be done.
It is not possible to pay Federal taxes due out of a state refund. You have to make your own arrangement to pay the Federal tax due. See this FAQ:
FAQ: How can I pay my Federal taxes?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/internal-revenue-service/pay-federal-tax...
