The War of 1812 didn't gain America much, as a country. It didn't address the complaints that led the Americans to declare war in the first place. We didn't conquer Canada. But we did gain a certain amount of what can be called our "national identity" after the war. Right at the heart of this was a new patriotic (and popular) song.
Most people today just use "go the way of the Whig Party" as an amusing way to say "disappear as a national political party." But a truer parallel to history would be to ask the question: "Will today's Republicans revert back to being the Whig Party?" Or, perhaps: "Will the Tea Party eventually go the way of the Whig Party?"