Edwards' proposal to terminate Congress's health care coverage if they fail to pass comprehensive reform is a good campaign strategy and a bad legislative strategy. On the one hand, there's no way such a bill would pass, and you don't want to start the battle for health reform with a legislative defeat on a symbolic measure. That said, as a rhetorical device, it allows Edwards to credibly ram home the point that Congress exists in a rarified realm where health coverage isn't an issue and attempts at reform can be weighed as mere abstractions, and it allows the public to get pissed at Congress for it.
There are two ways (which can, of course, be shaded and mixed) to construct a political strategy for passing health care reform. The first is to create a legislative strategy. Here, you identify congressional leaders and swing votes, think hard about what legislation could attract a coalition given the body's current makeup, bring the stakeholders in to pressure the representatives who listen to them, and try to wiggle and worm your way through the legislative process. This can be done with a certain amount of brute force, as Tom DeLay proved with Medicare Part D, or it can be a friendlier process,
The second way is to construct a popular strategy for for health care reform. In this conception, you don't spend a whole lot of time worrying about where Congress is, but instead thinking about where you can move it. You take your case to the people, engaging in a mix of hard-edged populism and grassroots organizing to ratchet up public pressure on members of Congress, such that they eventually grow afraid of opposing your bill and let it pass to save their seats. This is, for instance, how the Iraq War was sold.