While I am not a specialist in benefits law, the employer does not have a responsibility to coordinate, facilitate or assist in securing such applications.
Consult a local attorney, as he may be able to guide you in your efforts, and you may well want to seek alternative employment.
Please check the law of your state
It seems that you took this job, relying on the representations of your employer. You may have claims for for breach of contract and/or detrimental reliance. The problem you face is that: Even if your employer had fulfilled the promises they made, there is still no guaranty that you would have received the benefits; you must apply and could be denied. If you can show that you gave up other, higher paying jobs as a result of your reliance on the representations made to you, and if your reliance was reasonable based on the facts, you may still have a claim. There are other variables that need to be considered. Consider talking with an attorney.
Legal disclaimer: The answer provided: A) is for informational purposes only, B) is not intended to constitute legal advice, C) should not be relied upon in lieu of consultation with an attorney, and, D) does not establish an attorney client relationship. The answer may be different if all of the facts were known.