Which is why small government is the best solution.
The purpose of compromise in a democracy can never be realization of one's personal principles, which as you point out can never be compromised. Do you think the Founders would have designed the system to exclude principle? Of course not. Rather, the goal is a strictly human one, to leave everybody as happy as possible, or at least as little dissatisfied as possible, at the end of the day. That's what works in primate society.
At the end of the day, a person's own happiness depends on the man in the mirror. One's success and happiness depends on their own principles and how they apply them in life. Happiness can not be given by someone else or bestowed by the state, for it is a unique and personal experience. All the state can do is get out of the way so that the individual may pursue (or not) happiness in his or her own way. In the end, freedom is all up to the individual.