Great question shooter, realtiy is if your "lender" can't give you an answer on how long it will take for underwriting, you should RUN! I don't know who you are going with and/or what kind of organization it is, but as a national direct lender (we lend our own money and underwrite our files in house) I can tell my clients exactly how long it will be. With us, once all paperwork and appraisal is in, we close our loans in around 10 day.
Great part it, USDA appraisals are transferable and you already have all your paperwork so if you want to work with someone that can close your loan in a timely manner, feel free to contact me. I can walk you through the steps.