The shutdown happened once before in First Bush administration. Workers were paid later so no money was saved. It did not accomplish anything but cause anger. Don't know why the Republicans want to do it again.
As to passports DO NOT pay extra fees. Check at your local city hall. Should not take more than a couple weeks. Also get your photos at a drugstore that does passpost photos, usally ready in an hour. Be sure to renew on time as they expire in ten years. Be prepared for "interesting" likenesses in your photo. Mine looks vaguely like me! have fun on your trip.