I also broke one of the digitizer cable retaining flaps while replacing my iPad's LCD. After making sure that there were no pieces of the broken clip remaining, I tried just sliding the digitizer cable into it's housing slot, leaving it unclipped, and hoping for the best.
I was pleasantly surprised to find that the touch screen was accurately responsive about 95% of the time, with only intermittent registration of phantom touching. Of course, while that's better than I'd expected, it's far from ideal.
So I went back in, and used a small piece of polyimide tape in place of the clip, and haven't had any problems since. Of course, this was just a little while ago. Still waiting to see how long-term a fix this is. Worst case scenario, I suppose I could do a little light soldering.