There is no evidence of such a campaign.
Oh dear...
The issue of what happened in the 19th Century is not really germane to this thread, but I think I should clarify what I said above. That there is no evidence of a campaign of extermination does not imply that the actions of the United States and its people were wholly - or even largely - honorable. (It, of course, also does not imply the reverse.)
The basic statistics of all but the worst encounters between the parties in conflict (I'm trying to avoid terms like "Indian," "Native American," "native peoples," etc.) - such as the massacre at Sand Creek - do not bear out an intent to exterminate, even if they sometimes betray active hostility or, worse, a frightening indifference.
To take the example of perhaps the most notorious case of abuse, the Trail of Tears, roughly one quarter of the 16,000 persons forced to relocate (and subjected to other depredations and indignities) are believed to have perished, which means that circa three quarters of them survived in Army hands - the type of result that stems from cruelty and indifference, not from a campaign of extermination.
Other results are of similar character. At Wounded Knee, 204 Souix were killed or wounded by panicked Army fire, but so were roughly 60 American soldiers (the total is slightly higher, but some were killed or wounded by Souix who fought back) - indicative of stupid and reckless behavior, but not of an intent to exterminate. Archaelogical research at the Little Big Horn suggests that Custer's operational plan fell into disarry when he encountered a large number of civilians, whom he had the firepower to kill, but not the manpower to arrest - and chose to retreat.
That there was tremendous antipathy and often hostile intent is certain - and, make no mistake, such feelings existed on both sides where there was conflict, and led to a great deal of murder, evil, and tragedy. But there is no evidence of any large-scale intent to exterminate. Not on the part of the government of the United States, and not on the part of any of the other peoples of what is today our part of North America.
(Remember, too, that disease killed 85-95% of the pre-Columbian population of North America - a far more successful
accidental (on the whole) extermination than any intentionally genocidal human force has managed in the last several centuries.)