Carleton,
Don't use your thumbs, use the ridge of the pads of your knuckles to roll the tire on. For me it is like rolling my fingers into a fist around the tire. i use that ridge to grip the tire and roll the tire on.
All of the above only works if you get one bead on, and make sure the tube (slightly inflated) is centered over the rim, not half in half out. When you go to put the second bead on you have to start at the valve and work away from the valve. The valve area is the tightest area on the wheel.