Wrongful Termination? I was 39 minutes late when i clocked in...

On Wednesday 23, 2008, I had to be at work at 5:30am as always. My car wouldn't start. I called my work to let them know I would be late at about 5:18am. I was 39 minutes late when i clocked in. At the end of the day my boss asked me to his office where he told me it was unacceptable to be that late even though I have proof that my alternator gave out , witnesses, and the fact that i had called in before my shift began. He suspended me for 3-days w/o pay and said i would be on a 90-day probation period when I came back. He signed and dated the document stating just that, and then i signed to agree to those terms. On the third day of my suspension I was fired. I went to work the next day about 15 minutes early where I was told that they were letting me go because they don't need part-time help. I've been working full-time hours and i had a verbal agreement w/ my boss that I would have to work part-time hours when school started up again. I've been there for over a year. They are an at-will employer in New Mexico and I don't think its fair but I dont know whether it's legal or not? or if i should even care enough to take any action

[Bricks41]

The whole aspect behind "at-will" employment is that they can hire and/or fire at their choice. It will not prevent you seeking Unemployment Compensation. It is an unfortunate state of affairs but they can terminate or eliminate a position at will.