If your passport was lost/stolen, you need to contact the USA passport agency or state department as soon as is reasonable. They might t=advise you not to file a formal lost/stolen report immediately if there's some chance that the passport could reappear or be returned to you since once it's cancelled, this cannot be undone. However, if it was stolen a month ago, one could reasonably ask why this hasn't yet been reported. Also, do you have a police report documenting the theft from your (rental) car? This could be important, so step one should be to report the thief in the appropriate jurisdiction and obtain proof that this has been done.

My impression is that you should be able to get a new/replacement passport very quickly from a passport agency in the USA or a consultate if overseas. They can advise you regarding whether your passport card is linked to the passport or is still valid. However, since IIRC it's cheaper to request the passport card at the time you renew the passport, it might make sense to get a new passport card at this time also, depending on your current expiration date.

However, I'm a bit surprised that's you're not concerned about being without a passport for so long. Presumably you still have your driver's license, but I use my passport card frequently as photo ID and I would be concerned about not knowing whether it's still valid.