After 20 years, I'm changing out the kitchen faucet. Everything is disconnected except one very very tight nut. It's about 2/3 off. The gripping edges are broken. I've tried and tried with the plumbers wrench, but it won't budge. Part of the problem is that everything else is disconnected so it's now really hard to keep a grip. Then, I thought to cut it off, it simply won't fit in the space to cut it off (below). It also not fitting above; the escutcheon plate can be pulled up about 1/2 inch at an angle, but there isn't quite enough room. I tried adding a little soap to the top, but to no avail. What now? Is there some other method to try?
The nut is the old white plastic kind. I hope someone has some ideas because all the water for the house is off and that can't stay that way for much longer.

Get a hacksaw blade, put tape around a hand hold area and then cut a slot in the nut to release it.

I assume the problem is that the nut and shank of the faucet is recessed up behind the sink and is difficult to get to with any kind of tool.

Try drilling the nut into. Start with a small bit such as 1/4". Drill through the nylon nut as close to the shank as possible. After drilling through the nut, then ream the hole out toward the edge of the nut. Then move to a larger bit and repeat process until you have cut the nut into.

Another approach might be to drill lots of small holes through the nut, along side the shank, until the nut looses its grip.

Do as advised above: take a hacksaw and saw it off. Should go easily as you will be most likely cutting through brass or plastic.

Some hacksaws can have frame that allows you to set blade at 45 degree angle. That's a big help as the angle will keep your cutting hand above sink. Cut carefully so you don't scratch sink surface.

Good luck

Milo

We seem to be talking to ourselves here but after a moments thought, a multifunction tool ($20 from Harbor Freight) would make cutting a nylon nut away would be a 30 second job.