My Federal (and State) returns were accepted on May 1. It's June 2nd, now. I owed paid within a day of filing. Checking with IRS.gov, it says "taxes not processed." Why?

[pneumadeux]

I'm obviously not expecting a refund, since I owed (and paid already.) Should I just assume they're overwhelmed vs that there's a problem with my taxes?

[fanfare]

The Refund status page only works if you are getting a refund.

If you owe, you will see nothing. make sure your return is correct and pay the tax.

If there is an issue, IRS will contact you.

[pneumadeux]

Thank you for the reply. But I didn't go to the "refund status page;" I went to my Account page at IRS.gov.

It states, "Your 2020 Tax Return Is Not Processed." 

My return was accepted electronically by the IRS; got confirmation of that back on the first of May.

[fanfare]

you know the IRS is way backed up on processing returns, right?

I also went to my account and I see all my numbers, but no refund yet.

There is nothing you can do but wait.