Does my "tax due" amount come out of my tax return or bank account?

If you have federal tax due you do not have a federal refund.  And you cannot pay federal tax from a state refund.

Your state tax due cannot be paid from your federal refund. 

It is not possible to pay your state tax due from your federal refund, nor is it possible to pay a federal tax due from a state refund.  The federal and state treasuries are completely separate from each other.  You may have seen a TurboTax summary of your federal and state amounts that confused you into thinking one was “paying” the other.  It is not. The ONLY thing you can pay for from a federal refund is your TurboTax fees if you chose that option.  

 If you have federal tax due you can pay by mailing your payment with the 1040V voucher, (which has the address printed on it, having the payment taken out of a designated bank account, or you can pay directly on the IRS website. 

https://www.irs.gov/payments/direct-pay 

https://ttlc.intuit.com/community/tax-payments/help/how-can-i-pay-my-federal-taxes/00/26212

https://ttlc.intuit.com/community/tax-payments/help/how-do-i-pay-my-irs-tax-due-with-a-check-or-money-order/00/26403 

You must pay your state tax due using the state’s preferred method of receiving payment.  For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.

https://ttlc.intuit.com/questions/1900884-what-are-my-options-for-getting-my-state-refund-or-for-paying-any-state-taxes-i-owe

https://ttlc.intuit.com/questions/1901670-how-do-i-contact-my-state-department-of-revenue

we can not see your return.  it's not normal you have so much tax due based on $700 of income. there has to be more to your return.  if you can't afford to pay now you have until 4/15/2021 or the IRS offers various other payment options.

see this page on the IRS website

https://www.irs.gov/payments