The leaders of the various sometime colonies of Britain consider the possibility of a united entity, with the potential to be continent wide, but consider it too impractical to be set up, given the diversity of religious, political, and cultural aspects of the various states. The 'Swiss model' is considered and proposed to the decision makers of the various states. After deliberation, and what would now be called plebiscites of the voters (as in the UK only a fraction of the population is qualified to vote), a federated system is adopted. The FSNA expands piecemeal thereafter, with some of the Native American peoples able to negotiate local autonomy in their particular areas of habitation.
The background to the 'Louisiana Purchase' proceeded partially as in OTL: the mid-18th century transfer of territories east of the Mississippi to Great Britain: as Napoleon did not have the authority he was to achieve in OTL the area was not returned at the century's end. After negotiations initiated by Federal President Thomas Jefferson, France offered to sell the remainder to the FSNA. It took much lobbying on Jefferson's part, but the Parliament eventually agreed to the purchase.
The path of Texan independence from Mexico followed the course of OTL, but thereafter it became a largely independent state, having trade agreements with both Mexico and the FSNA that occasionally led to tensions arising from smuggling etc.
Slavery became increasingly an issue: its presence or absence much as in OTL, but with there being much less capability for exerting pressure by the federal authorities and between states. Industrialisation, the abolition of slavery in other countries and serfdom in Czarist Russia, and changing British policy after the so-called "Indian Mutiny" increased tensions over what should be done. Seccessionist tendencies increased and a number of states declared independence - but economic pressure (including that arising from British "pro-Northern" sympathies) led to the eventual ending of the crisis and the slaves being freed.