What if a car hits me when the pedestrian sign says "walk"?

I like to run around our town, and I make sure to use the pedestrian signal lights to cross streets to be safe. Well today when the light said "walk" I was beginning to run across on the crosswalk, and then i see a car come speeding up like it going to hit me, so I stop. But it stopped after it saw me stop in the middle of the crosswalk. Before that, there were several cars that did not even acknowledge that I could walk and kept on going. Don't pedestrians have the right of way? What if I were to get hit by a car one day, when the signal clearly said I was supposed to walk? Would it be my fault I guess for not looking carefully enough? Or the drivers for not obeying the traffic signal for pedestrians?