Many a Saturday project has ground to a halt because of a stuck nut. Get it moving with a socket wrench. (Pliers and adjustable wrenches are prone to stripping nuts.) Here's how Richard Trethewey, TOH's plumbing and heating expert, attacks the problem. If the first method fails, move on to the next:
Tighten. If you can get it moving, even in the wrong direction, you'll likely be able to reverse course.
Tap. A hammer blow can break a rusty bond. Use a nailset to focus the strike squarely on the nut.
Heat. Expand the metal by directing a hair dryer or a heat gun on it. Then give it a yank.
Lube. Clear away visible rust with a wire brush, then squirt Liquid Wrench on the threads. You may have to try several applications over 24 hours.