I believe ProxMox is already approved for gov use.
With that being said, the challenge is still adhering to the compliance. What this really boils down to is encryption support. Specifically, encryption support at the FIPS 140-3 level supported by the vendor for both data-at-rest and data-in-transit. So if Proxmox (or Debian) can provide the appropriate cyptographic libraries and the underlying volumes can be encrypted, and also network traffic encrypted, and also to to meet all of the other requirements than I don't think there would be issue with using the product. STIG the system as if it were vanilla Debian. I have personally STIG'ed Ubuntu to meet compliance; which is just another variant of Debian. Th most challenging part of the process was getting FIPS140-2 working. It required a license from Canonical and then to register that license with their online servers in order to gain the necessary libraries. I would think that getting enterprise support through ProxMox would be the best way to get this working... and with the issues VMWARE is having with the Broadcom takeover, it would behoove ProxMox to step in with that support at the enterprise level.