Nunya
How are the US going to get troops there? Without railways or handy rivers it is a very long way. Furthermore the US, because of its position and lack of any real enemies was able for most of its early years to maintain virtually no army. Britain has a world wide empire and hence needs to maintain forces all over the world.
The obvious answer would be that the US doesn't send troops out west, but instead uses them in the east. Capture a few important cities, and you're most of the way there. If you know you would struggle to keep them, sue for peace and trade them back for concessions out west. If you think you can hold them, do so and everything to the west becomes moot as you already de facto control them. These don't even have to be the major east coast cities (though they would be worth more): they can be western cities travelers would have to go through. Either way, once the west coast is gone inner Canada weakens for much the same reason the US required New Orleans: easy trade.
The big question would be whether the British have anything else on their plate. This isn't 1812 (I think) when it was grappeling with Napoleon. Nor is it Trent, when Britain is the undisputed master of all she surveys, and no power can counter her. If Britain is very distracted and can't spend the effort to blockade and fight the US, the US's chances go up.
Even successful though (and there's no guarantee), two butterflies immediatly stand out. There will likely be no Mexican War anytime, unless Mexico joins the fray for gains in Texas either now or later. Also, the Russians won't have the same impetus to sell Alaska to the US, becuase their real worry (Britain taking Alaska) won't be strong.