There were at least two issues that faced the federal government as a result of westward expansion during this time.
First, there was the issue of how to tie the country together economically. There were many calls for "internal improvements" such as roads that would have made commerce easier. However, this brought up issues of federal power and its limits. These issues helped to divide the earliest political parties.
Second, and more importantly, there was the issue of slavery. With westward expansion (in particular with the Louisiana Purchase) came the issue of whether the new territories and states would be free or slave. This issue caused conflict between the North and the South. In the early 1800s, it had to be resolved through the Missouri Compromise.