If I use {goblin tunneler}'s ability on a creature that has {fire breathing} on it can I then pump the creature up past a power of two and it still be unblockable.
Yup you can do the ability during declare combat and then pump before damage is dealt.
^
i used to do this with {Fiery Hellhound} completely devastating
Just don't breath fire in response to the tunneler's ability. Wait until after blockers. 8)