It doesn't mean wealthy people. It means people who feel they deserve to be a part of the elite, usually by virtue of their formal education. If we're "overproducing" such people, a large part of them cannot actually achieve this, because there's a lot more such people than available positions in the "true" elite (ie people having real wealth/power), which causes discontent.
Elite overproduction generally leads to more intra-elite competition that gradually undermines the spirit of cooperation, which is followed by ideological polarization and fragmentation of the political class. This happens because the more contenders there are, the more of them end up on the losing side. A large class of disgruntled elite-wannabes, often well-educated and highly capable, has been denied access to elite positions.
This however is also not a uniquely American problem.