USDA is not a lender, and mortgage rates are not going to soar - at least not according to my definition of that word.
Is your company providing relocation benefits? Do you own a home you need to sell? You can be pre-approved through a USDA Lender, and contract to purchase a home, and you can sign all the documents wherever you may be on the closing date.
The shutdown means that, once the lender has underwritten and approved your loan, it can not then go to USDA for their 2-3 week process. Basically, the file sits on a desk for 2-3 weeks, and when they get to it, they make sure it fits guidelines, and you proceed to closing.
My new USDA clients are opting for closing dates that are "on or before" 12/15, with a contingency for extension due to the shutdown.