These things happen from time to time. Though, it's especially sensitive as it sounds like it's a customer-oriented position. If you've been there a while and have a good track record, I wouldn't sweat it too much. No, I wouldn't think you deserve to be fired, unless you make this a habit. Whatever impact that may have had on the company's image can be easily rectified by simply by putting your best forward in the future, at all times.
Shoot, just last week I made the biggest employment-related error of my life. I went out drinking on a Thursday night, and events that transpired didn't put me in bed until almost 4:30 in the morning. I had to be up at 6....so, I set my alarm, thinking "this'll be a rough morning..." No idea how rough. Next thing I know, my phone's ringing, and it's my boss on the other end. It was 8:30, an hour and a half after I'm supposed to be at work, and...I'm still in bed. Was he pissed? No, he was extremely worried. Two years on the job and this is the first time I'd ever no-called, or even been late at all. I quickly apologized, asked for a half-hour, and washed up as best I could, made lunch, rushed out the door. Pretty sure I still smelled like an abandoned brewery. Good thing I don't normally interface with customers!
His response when I showed up? Concern, followed by laughter. Said it's something everyone does from time to time, no big. Sure, I'm positive it still affected my reputation a little, but a good track record made the difference in the end. And, it's not an experience I'm keen to repeat, I'll tell you that!!!
