One of the good reasons to have a Madisonian democracy, in which majorities don't necessarily win, is the intensity problem. When an intense minority is opposed by an indifferent majority, it is not at all clear that the indifferent majority should win. It is at least equally plausible that the democratic solution involves finding mechanisms for the intense minority to prevail in these situations.
From that angle, the way to understand drawn-out negotiations over complex legislation is that it's all about finding out what people actually do feel strongly about. Now, in some cases, it will turn out that both sides of an issue feel strongly about their positions, and if the issue doesn't allow for compromise, then someone is going to have to lose. But in many areas, one can find ways to slice the issue finely so that strong preferences are respected.
Thinking about Senate Finance and "death panels," what's going on is that we have a provision that most people think is benign but minor, while a handful of others claim that they're emassively outraged by it. Rather than sink the entire bill, the committee removes the offending provision. That's not a breakdown of democracy.
Of course, in this case, the whole thing is shadow play. People are pretending to be upset about a fictional provision in the bill, and so Senate Finance is going to pretend to remove it. The intense, but fictional, minority is going to prevail, but only in a fictional way.
Granted, it isn't exactly textbook democracy even in my version of the textbook, but it seems to me that it's a reasonable solution, rather than a terrible failure of our institutions.