During the War of 1812, the New England States and New York, which had already suffered a great deal under the previous adminstration of President Thomas Jefferson due to his Embargo Act, found themselves suffering again as war with Britain once again savaged their overseas trade. In OTL, there was all sorts of disloyal activity in the region during the war...States refusing to send their militia to help stop invasions of neighboring States, States allowing their citizens to sell supplies to British armies which were fighting American armies, even a proto-secession convention. Most, if not all of this, was actively organized by the Federalist Party, and this, in the postwar period, was a major factor in the collapse of said party.
But let's say the Federalists are a bit more organized and ambitious, and a bit more disloyal. They secretly negotiate with the British for support in mounting a coup against the government of President James Madison. The British supply arms and, in June 1815, the Royal Navy escorts a Federalist expedition which lands on the Maryland coast, depositing the Federalist strike force. The force moves rapidly, and before the government can react, is in Washington, where most of Congress and President Madison are captured and imprisoned. Vice President Elbridge Gerry anda minority of Congress manage to escape across the Potomac into Virginia. They flee to Richmond, and set up a temporary capital there.
Meanwhile, in Washington, a Federalist Rump Congress impeaches President Madison, and declares the President Pro-Tempore and the Speaker of the House (the next in line to the succession according to the 1792 Succession Act) to have vacated their seats. A Provisional Government, headed by Rufus King of New York, is declared, with a new election to be held "once a peace treaty with Great Britain has been signed, and domestic peace restored within the United States."
Of course, the United States Regular Army is completely embroiled against Great Britain at this time. It is likely the legitimate government under Gerry can call upon volunteers from the western and southern states which supported the war, and the Provisional Government under King can call on volunteers and militia from the northeastern states. So a civil war is likely.
So, how does it come out? Will the Gerry Administration try to cut a deal with the British? Will the British commit much in the way of forces to help the Provisionals, or will they take a more passive stance, simply keeping up pressure on the northern front so Gerry can't recall much of the regular army to help out in suppressing the rebellion?