The government is pretty much totally captured or killed in the war of 1812 when the British sack Washington, the states continue to fight after this and the war ends more or less OTL. After the war however things do not go well. A new Congress is formed and presidential elections are held with some random guy being elected the nations new president. However the new government wields very little power and individual states which since the war have been pretty much doing their own thing resist the governments authority.
The nation expands westward as per OTL, however rather than new states being created the solution is to simply add on to the territory of existing states. Slavery also expands and grows. Texas is established and forms its own government which becomes a major challenger in the region. Mexico and British North America gobble up the present US west coast and southwest.
In the 1860-1900s a civil war breaks out in the nation as territorial disputes and other issues spill over into open violence. The largely marginalised US Congress is seen as the way to end the war and some states pledge their support to the central government, forming a Continental army and unified military front against non Congressional forces and routing them. The nation after the war gives increased power to the President in an attempt to prevent a repeat of the war.
Just a quick and dirty idea. Another idea I had was having the country work somewhat like the Holy Roman empire, with the states being allowed a high degree of freedom.