"I've got mine" is an idiom
atic expression for the idea that if there is a possible injustice
in a situation, a privileged
person who won from within that flawed system doesn't really care because he/she
already got what they wanted. This reflects the common human failing to face problems unless they personally have been hit by them.
Example 1: Supreme Court Justice Clarence Thomas recently rejected arguments in favor of affirmative action, even though he personally benefitted from affirmative action programs in college. At the time some editorial cartoons showed him at the top of an affirmative action ladder, kicking it over as black students tried to climb up it. The system was of no importance now, because he had his.
Example 2: In my high school paper, a girl refuted the idea that the SATs are racially biased. Regardless of the quality of her evidence, it was important to realize that she got an 800 on the verbal section. The system worked great for her, so of course, from her perspective, it's not broken.
These two anecdotes illustrate somewhat different perspectives on the "I've got mine" mode of thinking. Someone motivated to make broad generalizations could say that Republicans suffer from this mind-set more than anyone else in American society. However, I would never say such a thing. :)