At the table in a heads up, I bet, he pushes all in. I turn my cards face up, without uttering CALL or FOLD. Are my cards still live?
I think Jon is correct in saying that it depends where you are, remember that whilst verbal declaration of intent is pretty much always the best way to do things, there are also rulings around physical motions as well. So argument is that by turning over your hand (provided you didn't make a forward motion, as in, throwing towards the muck) then it could constitute a call. HOWEVER, this could be viewed plain and simply as angle-shooting, because someone could turn over their cards, wait for a reaction, then say "Oh no I was folding, I didn't state I was calling". It's a slippery one.
I suspect if you were a noob and it was clear and obvious you didn't have experience at the table, you'd probably be fine, but otherwise you'd probably be chatting with the floor. But you'd only get away with it once.
Also I think it would depend on the size of the pot in question, in a large pot I suspect you'd probably get some hassle. Mainly down to the angle-shooting issue.