If a government shutdown were take effect at midnight tonight, April 8, the FDA and USDA essentials services would continue, however both would be operating under severe limitations.
According to the Congressional Research Service, essential services, such as, “activities essential to ensure continued public health and safety, including safe use of food and drugs and safe use of hazardous materials,” would likely be preserved. This is up to the Agencies, but if in the interest of public health, it is likely that those activities would continue, even if streamlined. According to CRS, they cannot comment specifically on the status of food safety inspections by FDA during a funding gap. The situation may be slightly different from that for meat and poultry (regulated by USDA Food Safety and Inspection Service), for which inspection is required in order for a product to be introduced into commerce. In both cases, however, it is up to the agencies and OMB to determine "excepted" positions.
A report by Dairyherd cites comments from a USDA official, who said that meat, egg and grain inspections are among services that would continue even if the federal government shut down, although most other USDA activities would halt. The inspections would continue because they are related to law enforcement, the protection of life and property, or are financed through other funding, such as through user fees, said the official who asked not to be named. USDA programs that would be suspended in a shutdown include farm loans and other farm payments, agriculture export credit and trade development activities and market news and statistical reports, he said, adding “Agency operational plans are still being finalized, but in the event of a government shutdown most USDA activities would be shut down or significantly reduced and most USDA employees would be furloughed."