Under the Indian Reorganization Act (IRA) Native American tribes had the opportunity to draft constitutions for self-government. These constitutions would take effect if approved by the Secretary of the Interior.
While, in theory, Indian nations in the US had always maintained a degree of soveriegnty, once on the reservations traditional social structures were eroded. Any attempts at preaching or maintaining traditional ways and ceremonies were viewed as dangerous by Indian Agents always seeing an uprising on the horizon. Traditional leaders were marginalized and often punished for speaking out while "progressives" who cooperated with the federal government, joined the Indian police, served on Indian courts, and spied on other tribal members, were rewarded.
This caused major schisms in Indian societies and a breakdown of the social structure which played a major roll in the growth of crime, alcoholism, and suicide.
While allowing Indians a modicum of self-determination, none of the governments formed under the IRA resembled anything near the traditional ways. The result was to further marginalize traditionals--a situation that continues to cause difficulties in modern times.
Wounded Knee II and the Leonard Peltier case were rooted in the traditionals v. progressives battle on the Pine Ridge Reservation. More recently, in 1999-2000 a grass-roots group took over the government building at Pine Ridge, forcing out members of the elected tribal council. Not long ago, a faction of Oneida--a tribe that has gained wealth through gaming and other operations--claimed that they were forced from their housing not because it was substandard and a health hazard, but to punish them for being traditionals opposed to gaming.
While many tribes function well under their IRA governments, it is not unusual for the legitimacy of tribal councils to come into question, and often governments are paralyzed during the sorting out. This can pose a danger to the financial stability, particularly of gaming tribes.
One could assume from this that Indians are incapable of self-government or it could be that the constitutional governments imposed upon them are like squeezing a foot accustomed to the moccasin into a leather boot. You can live with it, but it never feels quite like the right fit.