Native American tribes like the Lakotas, Cheyennes, Arapahos live in Black Hills of South Dakota. Mount Rushmore was a sacred place to them.
These tribes were not happy about the construction of Mount Rushmore in this location. Fat could not stop government because US government already declared this as national park and this location was under US government. So there was nothing that could stop them from making this project happen.
Till date native Americans use this place for the sacred purposes to carryout rituals. this very location of Mount Rushmore is still topic of discussion between US government and native Americans.