It works fine without maps or miniatures. I've DMed 3 sessions already without the use of either and we're having a blast.
If it's going to work, though, your players have to have total trust in your judgment of the battlefield and your decisions on whether or not they can pull off certain powers or feats that might be obvious looking at a map. As a rule of thumb, I usually favor the player, and avoid getting mired in the specific squares of movement so much as where they moved for or to. Your main focus is the pace of combat, which has to be quick and concievable even without the visuals.
That also makes your secondary concern open, detailed descriptions of battlefields, with enough material for players to work with and improvise off of. Don't worry about the exact size or distance of every little thing, reserve the numbers for enemies and any subsequent questions related to individual player moves.
If the players happen to slightly misinterpret what you've set up, add a chair in the bar fight or swing on a castle's chandelier when you didn't consider the possibility of there being one, again favor the player. Encourage the cinematic and allow the players to help flesh out the space. We've had a lot of fun with that, so long as they stay in reason (and they usually do, or will otherwise ask if there is something specific in which case you can decide).
Honestly, saving myself the time it takes to make maps and enjoying the fun of a shared creative process beyond what would have been on the paper or plotted with figures, it's a lot of fun. Not saying it's for everyone, but I've always been less focused on every little rule and more focused on the experience.
