At the moment, a federal court has ruled that California's Proposition 8 violates the US Constitution. Of course it's not a violation of the California constitution, since constitutional amendments by definition cannot violate their own document, but the US federal constitution trumps all state constitutions. That is the simple answer to the blanket statement that the will of the majority of California's voters has been set aside.
But let's move on. Assume that the pro-8 people are actually allowed to appeal. (Since the technical defendants in the case are state government officials who refuse to appeal the decision since they agree with the court's ruling, there's a good argument that the ruling can't actually be appealed, in which case it applies only to California, not even to the rest of the Ninth Circuit.) Assume that the Ninth Circuit Court of Appeals upholds the ruling at all stages, which extends the effect of the ruling to much of the Western United States, which will undoubtedly infuriate people in, say, Idaho, that much more.
Assume now that the US Supreme Court takes the case and upholds the ruling. (From what I've read, the court's swing vote, Justice Kennedy, would have to reverse his own opinions on a whole raft of issues to reverse the ruling.) This extends the ruling to the entire USA, and means that no state would be in a position to prohibit same-sex marriage.
But the game isn't over! Supporters of Prop-8-style law are absolutely convinced that a super-majority of Real Americans support them. (Probably because in their hearts many of them don't really believe that anyone who supports same-sex marriage is entitled to the rights of a human being, but let's leave that aside for now.) Supreme Court decisions can be overturned, too, by amendments to the US Constitution. They start pushing hard on their Defense of Marriage Amendment. But there, I think, they stall out. As I've previously written, I don't see them getting a two-thirds vote of both houses of Congress, and I definitely don't see them ever getting three-fourths of the states to ratify. If they could squeeze it through Congress, they'd possibly have a better shot at ratification if they required ratification by popularly-elected single-subject conventions the way the 21st Amendment was ratified, but even that would be difficult.
And there you reach the end of the road as far as ordinary politics is concerned. Prop 8's supporters can go to no higher court, and the governmental/constitutional amendment process would be exhausted. What happens if the supporters still don't give up and live with the new order?
Well, there's a long-term possibility of slowly trying to get legislators elected who will do things their way, but that takes many years and is likely to try their patience unduly. Anything else?
Well, yes. In a word: Revolution.
No, I'm serious. This entire country was built on a rebellion against lawfully constituted authority. When every possible legal and political avenue is exhausted, the only choices you have left are to acquiesce or to revolt. And I don't mean wave signs and pretend you have much in common with Boston's revolutionaries of the 1770s. I mean declare your independence and be prepared to back it by force of arms if necessary. I actually think the Second Amendment is as much about preserving the "right of revolution" as anything else.
Would it work? Of course not! Among other things, I don't think you could get any governmental unit of sufficient size to support it. The US civil war started when the first level of government below the federal one — individual states — stated declaring their own independence, and those states had sufficient governmental infrastructure to make it stick for a while (almost five years). And since even that didn't work, I can't see a bunch of armed individuals managing to create their own country. It might be painful, even deadly, but it wouldn't work. However, if people are sufficiently blinded as to the rightness of their cause, they'll do stupid things.
Do I really think that the far-right-wing is sufficiently nutty as to stage an honest-to-goodness armed revolution? No, I don't think so, although I'm sure there are individuals who would welcome it gladly. But it's unwise to forget completely about the possibilities, and I think any person who understands US history should realize that when you run out of every other option, violence really is the last resort. But you had better be really sure of yourself if you try it, since going all-in on that political bet puts more on the line than just a few chips.
The last line of the US Declaration of Independence ends "...we mutually pledge to each other our lives, our fortunes and our sacred honor." Those were not empty words. They were to be taken literally; yes, really literally, including "lives." Revolt against the government and you either win (in which case you are by definition right -- "Revolutions are always legal in the first person") or you very likely die ("it is only in the third person that they're illegal").