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According to wikipedia, during the President James Madison and most of the federal government had been present at the Battle of Bladensburg during the War of 1812. Obviously, in RL they were not captured. For those that would like more information: Bladensburg is in Maryland and the battle is the even in the war immediately preceding the Burning of Washington

My questions are as follows:
Would it be possible to capture Madison during the battle?
If he is captured how would this play out for the war?
Would the British be able to force through a favourable peace treaty?
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