Well, before word of the British "victory" got to both sides, when they still thought the war was on and the United States forces were fighting under the illusion that they might win, there was a fairly significant "skirmish" down New Orleans way in 1814 where Andy Jackson acted out his illusions of victory.
Had a treaty not been signed by that date, I submit that that victory would have insured that the British would have relented anyway.
Jeff, look at the history objectively. The British achieved their goals. The Americans achieved NONE of theirs. Period. End of story, so let's concentrate on (a) the British didn't reincorporate America into the empire (never mind that such was NOT their objective) and (b) a few insignificant frigate actions that we won (because we don't want to admit that we lost all of our overseas commerce).
Like I said, we lost the war. We also lost in Vietnam. And Bill Clinton got impeached. Reagan Won the Cold War. Thus endeth the class in America History 565, What the History Textbooks Don't Like to Talk About.