Questions of whether the chamber's apportionment is fair would immediately come up, for one thing. A lot of reservations have very small numbers of enrolled members (literally like 100-200 total). Others have well over 100,000.
If you think the population difference between California and Wyoming is extreme, take a look at the Navajo Nation vs. the United Auburn Indian Community.
This would be structured like the Senate; each tribe would get 2 representatives. The same questions of fairness the Senate would have would apply to this chamber, too.