Here's my thought - the US successfully annexes Canada in the Revolution, after the Quebec Act never passed in 1774. The US takes the entirety of North America over the next century. During the Mexican-American War, President Polk supported the Yucatan republic and Rio Grande republics, bringing them in as states, countering with two new Canadian states in the North. Bitter over losses, another Mex-American war in 1853 begins after the Gadsden Purchase, in which the US takes all of Mexico. The US now has a load of land, and the population can spread out across the continent. The railroads connect the US faster due to the spread of the US, and more cities spring up along those lines. Keep up the European immigration and you can speed up population growth, plus the former Mexicans.
James