Prior to the Louisiana Purchase, the concept of manifest destiny was unknown for the most part. As such, I do not think the slaveholding political class thought too much about continuing the expansion of slavery as a means of keeping political power. While they certainly fought hard during the constitutional convention for protections of slavery, they did not get complete protection of the slave trade and saw it outlawed by 1808. Obviously the 3/5 compromise at least kept the white population of the South overrepresented in congress (so that would be seen as a political win). But the Northwest Ordinance which made that new territory free from slavery, could have probably been successfully opposed by the congressmen and senators from slaveholding states, had they had the benefit of hindsight.
In 1803, without the territories brought into the US by the Louisiana Purchase, there were 8 slave states and 9 free states (Ohio admitted in 1802, I think). The territory that would become the states of Alabama and Mississippi were obviously destined to become slave states, since it was being settled primarily with people from slave states. While the the Northwest Territory was being settled by free soilers. In OTL, once Louisiana was purchased, the state of Louisiana became the next state to once again balance free and slave states.
If you cut off the further expansion of the United States, either, Mississippi and Alabama get carved up into more than two states, or it takes a long time before more free states are admitted out of the Northwest territory.
So my gut tells me that without Louisiana, you have faster and denser settlement in Mississippi and Alabama. Since Louisiana was already a developed slaveholding territory (only French/Spanish), I bet you still have alot of Americans immigrate there with their slaves. In addition, freesoilers start filling up Indiana, Illinois, Michigan, and Wisconsin. There will be numerous efforts to try to continue the balance between free and slave states. Once all territories have been admitted as states (including Florida, if it can be acquired), issues regarding slavery, tariffs, fugitive slave laws, etc., will eventually lead to secession movements probably as early as the 1830s. Then depending on who the President is will determine if there is a war or whether states are allowed to peacefully secede.