As one who has helped organize some class action lawsuits (against cigarette companies), its not very easy to do, and the biggest difficulty is finding a lawyer/lawfirm willing to take the case (as the cases are very expensive, can take many years, and the lawyers only get reimbursed for costs and paid if they win the case).
Also, since US Congress enacted the Class Action Fairness Act six or seven years ago, its far more difficult to win class action lawsuits than in the past.
I'm also not aware of any class action lawsuits that have ever succeeded (or that have been filed) against a government agency.