Can I sue my current employer for refusing to pay me the hourly wage I was promised?

I was working part time for some extra money and was offered a salary match to come work there full time. They also stated that they were working on a health insurance package. I turned in notice to my other job and just before I was to start full time but after my other position was filled I was told they would not honor the $12/hr. I never even got the 9/hr I was quoted for part time. I'm beyond stressed out over this as. I am financially destroyed and have no idea how I am suppose to pay my mortgage and eat only making $8.10/hr. This just cannot be right. I'm stuck with a worthless job until I can find something else. I didn't ask for the full time position it was offered to me.