Erm, you realize this is a thread about gay marriage right? Marriage has always been between a man and a woman, and until recently it wasn't even considered that it might be otherwise. So not suddenly changing that is not a step away from republicanism, since we started there to begin with. Especially since if gay marriage is made legal democratically, it will be through elected representatives, i.e. republicanism.
Your post is irrelevant anyways. The public votes on its government; its government votes on its laws. The will of the people matters there.
Democratic protocol and procedure is incidental to republicanism. Have been, both in theory and practice, since Aristotle.
Republics can be oligarchies, rule of the few and wealthy, even despotic governments (rule of one). The only essential quality of a republic is that it invests legitimacy and power into principle (aka, a Constitution) rather than in the decisions of an entity (a king, corporate executives, or an assembly of citizens).
That is, medieval nations are not republics because their kings and nobles abide by High Justice, a variety of justice where any rules and protocol are provisional and optional; things like "innocence before guilt" and "due process" and "private property" exist at the discretion of the decision-making of a single person (they can either not exist at all, or be suspended at the convenience of the judges and executors) -- in good cases, their compassionate, reasoned judgment of what is best for the people of their country, in bad cases, at his whims and tantrums.
Most of the democracies of Ancient Greece were not republics either, because they have a very limited sense of civil rights and liberties; the only freedoms allowed, and duties prescribed, are those agreed upon by the collective at any given point in time. That is, no real freedom and no definite duties, no genuine principle or law. Hence, when several generals failed to achieve optimal results on the battlefield, the Athenians decided to deprive them of due process and summarily executed them.
Ancient Rome was a republic, which employed democracy minimally. The people were allowed to run in/vote for some public offices, but the higher offices were restricted to the Patricians (aka, the noble born), which was oligarchy (rule of the few). However, this was because it was believed (argued) that Patricians had the character and skill necessary to administrate a free society with property rights; it was beleived that because Patricians were outnumbered by commoners and had a lot of property and freedom to lose, that they would be eager to put their advanced education and resources to defend the principles that Roman society was founded on. So, Ancient Rome combined democratic and oligarchic functions.
And the Founding Fathers (who used Ancient Rome was a model) founded their government on law and principle; this is what makes the United States of America a republic. They reasoned democratic functions were more useful and necessary than the Romans believed, but they also felt a tyranny of the majority would pose a danger to their cherished principles. So, they designed the government to frustrate majorities, while not depriving them totally of power.
Unfortunately, it isn't perfect.
Bottom line is, the will of the people is not valuable in and of itself (for that matter, I don't think it even exists).