Whenever you have social programs designed to help victims of genuine misfortune, there are always going to be some who will abuse those programs. Obviously, you do all you can to minimize such abuses. Yes, seeing people bilk the system is infuriating, but I'm not willing, for example, to penalize poor children even in cases where their parents are largely to blame for their own predicament. And I'm certainly not willing to withold help from people who are sick or unemployed through no fault of their own because a few get benefits they don't deserve.
I also think ApatheticNoMore raises an excellent point about differing levels of fraud. I don't like paying taxes to support welfare, but I dislike paying taxes to support corporate welfare even more. Five years ago gangs of crooks in the financial industry brought the world economy to the brink of collapse and the taxpayers bailed them out. To date, there hasn't been a single criminal action brought against any of these bozos. Seeing this, a worker with a mild injury milking Social Security disability might be excused for not feeling terribly guilty.