I have filed my 2019 taxes and owe roughly $2500. I provided a card to charge when I filed, when can I expect it to be charged so I know my taxes are paid?

you can pay the TurboTax fee with a card, but not your income tax.

go here to pay with a card - www.irs.gov/payments

In the FILE tab step 1 you paid for the TT program  and then in step 2 you choose an option on how to pay the FED  balance due and that info is passed to the IRS and THEY  not TT completes the debit/charge.  If your return was rejected and you had to mail in the return then the payment info was never successfully sent. 

Before you pay on the IRS site please review what you entered in the program. Log in and scroll down and click on ADD A STATE  to open the account then WITHOUT making any changes check the option you choose in the FILE tab ... also save a PDF of the return (with and without the worksheets) for your records using the Print Center in the black toolbar on the left.  If you just recently filed successfully it could take the IRS a week or 2 to complete the transaction. 

If you did not set up a payment correctly then you can make the payment online directly on the IRS site :  www.IRS.gov/payments