How do you approach pricing when a client wants more than their budget allows?

I think the best thing to do is give them options and break things out as much as you can. It should always be more about scope reduction than it should be about lowering your price. Another option could be switching their finish materials up to a different brand.

Depending on your business, you could have them do some of the work themselves also. If you're running things smoothly, you'll have your shopping lists already. Just be like, I can give you this list and you pay for and deliver these products to the site. You'll save on the mobilization then just be charging labor which is where we make all of our money anyway (this is just me though so maybe you make a lot on materials). 

One thing we NEVER compromise on is rough materials. Like in a shower, I'm not going to use concrete board and red guard. I don't need the job that bad. 

Another thing you need to offer is financing. 

Sometimes people just need a reality check too. Can you get it done for cheaper? Probably. But I'm not just offering you (fill in product here). I'm also selling you the experience. Making things easier on you.