It would eventually end too. What were there? Seven million people in Mexico at the time? With millions of immigrants coming in from Europe, their population would be overwhelmed by people who are more inclined to the Union. It'd be the same with Canada, though Mexico having more people would mean it might take a couple generation for assimilation to be complete. It would be intigrated by 1900. Depending on how 'unstable' Mexico was in that other timeline, some regions might look more favorably on DC than MC. Of course those would likely be the periphery states and territories.
Of course, thanks to slavery, if the US annexed Mexico, the North would be screaming to annex Canada so there would be room for free States to grow and maintain that balance in the Senate. Up until the Civil War, both sides were obsessed with it.
The US would still have to commit itself to decades of occupation. Also, why should Mexico be slave States? Mexico had outlawed slavery.