My opponent attacks me with a Sludge Crawler. I have a Smite the Monstrous in my hand. I do not declare any blockers for the Sludge Crawler. My opponent then pays 6 to pump the Sludge Crawler up to 4/4. Do I have an opportunity to play Smite the Monstrous before combat damage is dealt? It would seem that if I play it as a direct response to the Sludge Crawler's activated ability, it would go on the top of the stack on top of the Sludge Crawler's activated ability, then fizzle because its target is not legal (yet). Then the Sludge Crawler's activated ability would trigger, but then I would take 4 damage because my Smite the Monstrous had already fizzled.
Typically when I'm playing, neither I nor my opponent announce each of the combat sub-phases (http://mtgsalvation.gamepedia.com/Combat_phase) explicitly other than declaring attackers and blockers. I'm assuming in the case above my opponent used the Crawler's ability at the end of the Declare Blockers step. Would it matter if they had used it then or at the beginning of the Combat Damage step for the purposes of determining whether or not I can play Smite the Monstrous?.
No step or phase can end until both players have passed priority with the stack being empty. What this means for you is that you wouldn't need to cast Smite the Monstrousin response to the Crawler's activated ability; you can wait for the abilities to resolve, then Smite it before damage is dealt. You do need to cast your spell before the Combat Damage step, because the first part of that step is the actual combat damage.
Note that it would be impossible for your spell to "fizzle" in this scenario. "Fizzling", while not an actual official term in Magic, means that your spell was countered due to its target becoming illegal after the spell was cast. Spellcasting legality is checked both when the spell is originally cast AND when it would begin to resolve, so if you had attempted to Smite a creature with power less than 4, your spell would be illegal right off the bat and you'd simply rewind the game and return your spell to your hand, since your action was illegal. You aren't punished for this, beyond informing your opponent that you have a Smite in hand. Now, if you attempted to Smite an opponent's 4/4 and they cast Bile Blight on their own creature in response, your Smite would indeed "fizzle" and be countered.
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Formerly Angrypossum over at the now-defunct WotC forums.
Typically when I'm playing, neither I nor my opponent announce each of the combat sub-phases (http://mtgsalvation.gamepedia.com/Combat_phase) explicitly other than declaring attackers and blockers. I'm assuming in the case above my opponent used the Crawler's ability at the end of the Declare Blockers step. Would it matter if they had used it then or at the beginning of the Combat Damage step for the purposes of determining whether or not I can play Smite the Monstrous?.
Note that it would be impossible for your spell to "fizzle" in this scenario. "Fizzling", while not an actual official term in Magic, means that your spell was countered due to its target becoming illegal after the spell was cast. Spellcasting legality is checked both when the spell is originally cast AND when it would begin to resolve, so if you had attempted to Smite a creature with power less than 4, your spell would be illegal right off the bat and you'd simply rewind the game and return your spell to your hand, since your action was illegal. You aren't punished for this, beyond informing your opponent that you have a Smite in hand. Now, if you attempted to Smite an opponent's 4/4 and they cast Bile Blight on their own creature in response, your Smite would indeed "fizzle" and be countered.