Can you sue? Sure.
Will it impact on future immigration options? Probably not.
Could it result in you being arrested now? Maybe, if the employer 'blows' the whistle on you.
Hire a lawyer.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
Since you are not currently authorized to work in the US you'd be taking the risk that that fact would come to light. There may be some protection from deportation available for whistle-blowers who are undocumented. Hire an immigration attorney who is knowledgeable in employment/labor law, or get an additional opinion from an employment/labor law attorney.
Gunda J. Brost
Brost Law Office
This advice does not form an attorney-client relationship and is merely informative. It should not by itself be relied upon to address a legal concern.