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.
No, Hobby Lobby, that quote on your website is NOT from Thomas Jefferson! And, furthermore, the document it comes from -- which was written by James Madison -- is a list of some of the best arguments AGAINST that Supreme Court ruling that you and your fellow Christian supremacists are currently gloating about.