I didn't have problems finding work. It's really all about who you know IMO. Once you get your foot in the door, its up to you. My stutter isn't that severe compared to some I know, but whenever I meet people and they hear me stutter, I usually apologize and say I have a speech impediment. I never met anyone who judged me for it, or who cut me off. My advice and although its tough is try to relax and speak slowly. I know that is easier said than done, but it has worked for me thus far. If you feel it's really holding you back, then perhaps see a speech pathologist.