[Don H]

Tribal Sovereignty as a Paradox
While the U.S. government recognizes American Indian Tribes as sovereign nations, the U.S. congress is recognized by the courts as having the right to limit the sovereign powers of tribes. However, Congress must do so in definite terms and not by implication.

What Does This Mean?

Tribes remain sovereign nations and possess self-government.
Tribes have a nation-to-nation relationship with the U.S. federal government.
Only Congres has plenary (overriding) power over Indian affairs.
State governance is generally not permitted within reservations.

http://www.airpi.org/pubs/indinsov.html