What's worse is that not breathing, is a sign of tension not just in your lungs but your muscles as well.
Best thing I would do in a situation like that is to stop, take a short break, slow down the piece a lot until it's completely comfortable to play no matter how slow, or how difficult the package is. Focus on relaxing, then as you master it, shift the focus more into the music, and speed up slowly.
I have found that over the past year, the tension in my arms\shoulders and breathing has decreased. And because of this, the guitar feels more comfortable in my hands when play.