Ah! I hate the stammering thing. Thankfully that doesn't happen very often, but when it does it is usually after having to talk with a lot of people.
Once, we had been quite busy at work and I was attempting to ask a woman if she would like a bag. I was not feeling particularly overwhelmed, as the rush had given way to a few moments of quiet nothing and she was the only customer in our small store at the moment. With that being said, you can imagine my surprise when the phrase "Would you like your item bagged?" came out in a series of unintelligible sounds. It is as though my brain said "You know what? I'm tired of words. Let's just make sounds and see what happens."
I spent a good five minutes trying to ask the poor woman until finally I just pointed at a bag. She smiled, said "no", and was off on her merry way. She was very nice and didn't seem annoyed in the slightest.