I am a US-(another country) dual citizen currently living in the States. The only forms of ID I have right now are the US and non-US passports.

Naturally, the latter has no US visa in it. I need to renew my US passport right now (urgently), so I will not have my US passport for the next month. I also need to fly domestically during that time. Would I be able to use my non-US passport as ID in the airport, or would they be concerned with the lack of a visa in it?

I do not have a US driver's license or state ID to use as an alternative.