The greatest problem facing the united states during the period of "manifest destiny" was

The answer is: whether slavery would expand across the United States,

Manifest destiny Refers to the view that United States was destined by Gods to conquer all the territories in the north american continent.

This view originated from the southern colonies in mid 1800s. At that time, people worried that this view could lead to military expansion on northern states and expand the practice of slavery to these areas.

the tallest building in the western hemisphere and the sixth tallest building in the world