The Native Americans faced numerous problems in trying to preserve their hold on tribal lands and, for that matter, their very existence as humans. Diseases such as Small Pox caused up to 90% mortality rates in tribes after the initial contact with Americans, and the government sometimes used disease as an extermination tactic.
On top of this was the crush of white Americans moving west in ever increasing numbers, not to mention the construction of railroads and the dispatching of army troops to "protect" settlements, often by killing off whole populations.
Then there were the treaty agreements with the US government and the tribes who chose not to resist. As the treaties were seldom honored, Natives still lost their land, or the best parts of it anyway, and were forced onto reservations.