I don't think you should ever force anyone to be an organ donor. Some people have religious reasons for refusing to be an organ donor, and it goes against our American principles to force them. I do think it would be useful to have some kind of incentive to make people more likely to sign up to be an organ donor, though.
Dead or not, my organs are my own, and if I choose to take them to my grave, that is my right. We can cure disease and seek to end all war, but the world population is still growing faster than it can be fed and watered. We shouldn't require those who don't believe organ donation is the right thing to do to partake in the unnecessary promulgation of the species.
Major religious groups oppose organ donors. The Catholic Church, evangelical Christians, and many, many other religions say that you cannot buy or sell the body. It's not yours to sell, and we can't support a system of organ donation if there is going to be a market. Some of you who are watching may be saying, "What do I care? They don't have to participate." But remember that hearts, livers, and other organs are always going to come from altruistic donation. If one part of the system becomes a market -- for example, kidneys -- and everybody else withdraws from the rest of organ donation, we may wind up killing more people than helping them benefit.
Forcing people to become organ donors violates their civil rights and civil liberties. It is a violation of freedom of person. Some people can not donate organs because of religious reasons and forcing them to do so would violate religious freedoms. This is a bad idea and would cause lots of problems.