The real skill, as some have said, is in knowing which moves aren't worth considering, and which moves need special attention, and then rendering an accurate evaluation of the future position you're visualizing.
I agree. Time spent analyzing unproductive moves is the mark of a weak player.
Indeed, that's precisely why an 800 blitz player cannot be over 2000 in correspondence without assistance. There's just not enough time to analyze 25 poor moves in every position. The 800 blitz player favors poor moves.
I can see 3 moves if I concentrate, but sometimes I go up to 6 or 7. That's not all possible permutations, though, just the few most possible routes. 3 is the number I operate with.