I'd try a tough canvas or denim, but do try to (gently) train them to leave even that alone. My cat stopped sculpting our furniture when we got one of those flat cardboard scratching posts. (I read that cats "need" to scratch, the way dogs need to chew.) Make sure to get a nice, wide one: http://www.petco.com/product/104528/PETCO-Cat-Double-Wide-Cardboard-Scratcher.aspx

Yes, I had canvas in mind. What about the army duck fabric from Restoration Hardware? (Is that essentially canvas? I have to go to the store and check it out.)

The cats have lots of scratching posts, but I think they go at the furniture to spite me. My velvet sofa has held up surprisingly well. There are tiny pock marks in it, but no tears and nothing is visible from more than a foot or two away. I just don't want everything to be velvet.

Yes, I think army duck would also work. Have you already considered slipcovers? Because they can fit more loosely than traditional upholstery, there's nothing very fun for little paws to grab onto.