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Not every file is looked at today and approved today.
USDA is not known for there speed.
You still have time to close for April 1st, just any conditions you need to respond back ASAP.
No conditions from USDA, but can possibly still get conditions from Lender once file comes back. Rare once they send file into USDA, but possible.
The chance for USDA to deny loan once submitted from Lender, is super slim. You should be good to go...