What makes law legitimate under our system? The standard answer, which I'll call the "Madisonian Formula," is that all three branches must agree. This is true for most statutes (unless they involve a non-justiciable matter) and for many Supreme Court cases, which will not go anywhere unless they receive at least some support from Congress and from the Executive Branch.
The agreement of all three branches, though, is a necessary and not always a sufficient condition for legitimacy. For example, any law that touched on slavery required the consent of North and South prior to 1861. While the Constitution said nothing about this, our institutions adapted to express this understanding. There was a longstanding custom that there be an equal number of free and slave states so that the Senate would be equally balanced. The slavery compromises in 1820 and 1850 required long and complex sectional negotiations. When a Northern party won the White House in 1860, the South considered that cause for secession. Indeed, one could say that Reconstruction's violation of the anti-sectional rule explains the failure of the Fourteenth and Fifteenth Amendments to transform race relations in the South.
A distinctive feature of the Obama Administration is that there seems to be an extra-constitutional principle developing that says the consent of both parties is required for legitimacy. (There are some precedents for this, but let's leave that for another post). The lack of bipartisanship is a crucial part of the criticism of the Affordable Care Act ("It was passed only with Democratic votes.") An anti-partisan norm also explains why Chief Justice Roberts may have felt pressured to vote how he did in Sebelius (in other words, striking down such a law only with GOP votes would have been illegitimate.) Indeed, when I talk to non-lawyers, I'm struck at how important they think bipartisan agreement is as compared to how unimportant it is for lawyers. Hence my attempt in the Washington Post op-ed to translate that into a notion of "settled" law.
One final thought is that the idea of bipartisanship as essential explains the changes to the Senate filibuster. I've railed against this and so have many others. So why do so many people disagree? When I ask non-lawyers, they say that they like a sixty-vote rule in the Senate because it forces the majority party to get some votes from the other party. This is not part of "How a Bill Becomes a Law." But it is a part of the living Constitution.