Although I think you can get away with 4 inches (not sure), 6 or more inches really looks the best. Do you already have the tub and are you taking into consideration the molding around the door? An oval tub will taper at the ends and you can shape the deck that way as well. That's what we did.

Aren't you saying that you only have 1 1/2" clearance, though? A 36" wide tub to fit into 37 1/2" space?

That's a pretty close call. I would defer to the experts, but it seems that at best your tub would be jammed against the wall, and the front would need a self-apron, not a tile deck. But what do I know? :) Best of luck.

Would a narrower tub work for you?

I think you "can" but it will look pretty squished/cramped. When I was touring parade homes last year, some master baths had whirlpool tubs without much deck, and they really looked squeezed in, making the bathroom look crowded rather than spacious. In my mind it was a detractor to the look of the room.

Of course it does make a difference how the rest of the room is. If it's a small room to start with, and a tub with a small deck is to scale with the rest, then you'll be ok.

So long as you have a few inches on all 4 sides, you're fine, from a technical standpoint.

Of course, as with many things, bigger is better. :-)

Molly,
Not really related to your issue, but do you happen to know the specs of your tub? How many gallons it will hold?