Nevermind. I figured out the problem. I did not include in the popup one of the list fields that was set as “required” in MailChimp.
So, the solution is to either add the required field to the popup, or change the settings in MailChimp so that the missing field is not required to have a contact added to the mailing list.
I chose to change the MailChimp settings so that the field missing from the popup is no longer required.
It is now working.