You can use Anti-Icky Poo on top of Nature's Miracle. They're both enzyme cleaners (it just really gets hard when you set the urine with a regular household cleaner - because that's all they do.

Soap & water didn't detract from what the enzyme cleaners will do, however). Trust me, Nature's Miracle won't do it. And you'll probably need to treat it at least once more, if not twice.
Things like a couch and mattresses are harder than floors because of that third dimension - depth. We had a kitty with a problem that peed on the couch several times, and it always took 3 treatments to get the smell out. The problem is that cat pee wicks, and to get the smell out, you have to get the enzyme cleaner to all the same places the cat pee went. So you have to really soak it - and even then, you don't necessarily get the enzyme cleaner to all the same places on the first go round.
Our kitty peed on the cushions, and it didn't make it down to the frame. We tried pouring the enzyme cleaner on the cushion - in the end, we really had to soak it. I'm not quite sure how we had to use about gallon of enzyme cleaner to clean up what must have been a cup or less of cat pee LOL, but .... the bottom line is that spraying the surface won't do it. You have to get it down in there.

And if you do it right - it can take days to dry (especially if it's humid).
But if you want to get at it with the Nature's Miracle while waiting for the Anti-Icky poo, you won't make the Anti-Icky poo less effective.