Yes, on foods that have a standard of identity such as most dairy/milk products will have microbiological standards. I am not aware of any other foods under the US FDA that have microbiological standards, aside from "pathogen negative".
The USDA though...they may have standards. I have no experience in USDA and that regulatory body for the products under them so I can't comment on that aspect. For what it is worth, the USDA has oversight of meats, except fish (US FDA), eggs, some milk/dairy (dry powders for export).
The US regulations can be quite complicated and cumbersome...I really wish they would move it to one agency only and have standards across the board. That's wishful thinking though...lots of lobbying goes on here in the states.
Actually, i think there are micro.standards for some products for (FDA) import purposes as discussed previously here but no idea regarding the category you mention. Some searching maybe required.