If I recall correctly it wasn't an entire tribe, but rather a smaller group of people lead by Chief Leader Sitting Bull. One year prior to their attempted fleeing of US territory, the Battle of Little Big Horn took place in Montana against the 7th Cavalry which resulted in the deaths of George Custer and five troops. It was Lakota and Northern Cheyenne who fought. Sitting Bull feared retaliation for their victory and that's why they were trying to leave. I think they were called the Hunkpapa Lakota, a branching of the Native Lakota. I hope this helps somewhat.
FDR's New Deal was successful at combating the Great Depression. After implementing his New Deal policies, the unemployment rate dropped by roughly 10% in the first few years. Along with this, the programs helped to build America's infrastructure, parks, and resulted in the creation of several long term agencies that exist today (like the SEC and FDIC).
The New Deal affected future generations by creating agencies that still exist today. A perfect example is the Social Security Administration. This gives financial assistance to America's elderly population. This system is one that most employees currently pay into. This has been seen as a successful program, as it helps to pay for several different things (like medical costs) that senior citizens would otherwise struggle to pay for.