Generally, with pasta you want the hardest flour you can get, and at a very fine grind. The standard whites are a type called 00, which is very hard indeed and semolina -- also extremely hard. The problem with whole wheat flour isn't the protein content, it's the texture and the fact that whole wheat glutens just don't seem to want to stretch as much. In fact, the more rough handling dough receives the more a high protein level helps -- and with all the rolling required to get it thin, pasta wants heap plenty protein.
The best advice I can give you is to use 1/3 or 1/2 white or semolina flour. Whether you do that or not, try the following tricks: Compared to a semolina or white flour pasta, cut down the egg amount by a 1/3 to 1/2 (coincidence, I swear it).
Whole wheat doughs will come together without a lot of liquid and be very stiff. Stiff doughs are fragile -- and that was your complaint. Better to make a soft (wet) dough, and if it's a tad too wet, knead some extra flour in during the kneading period.
Use the volcano method rather than the processor to mix and form the dough if you can possibly spare the time. Your sense of touch will help you get the dough exactly right -- especially after you've done it a few times.
Knead, knead, and knead some more. You want to make the dough as elastic as possible by developing the glutens and stretching the heck out of them. Hand kneading is better than machine for extended kneading, because it puts less heat in the dough. If you sense any fragility or stickiness, rest the dough in the refrigerator between stages.
You can use the processor to mix and knead -- but you lose a lot of control and add some undesirable changes. A stand mixer is better than a processor but still not as good as your hands. Do you watch Iron Chef? Even in the heat of battle in Kitchen Stadum, the contestants usually mix and knead the dough by hand. Now you know why.
There are limits to how far you can push whole wheat glutents before they become uncooperative. Compared to a white flour dough, allow at least one extra rest in the fridge; and allow the rest(s) to go an extra 10 minutes.
I know each of these techniques is time-consuming, but what are you gonna do?