You might look into Chinese Pod at www.chinesepod.com.

Consider a "Subscription" at the Basic level for $14. Then you can choose from the Beginner lessons at your convenience, do it at home, in the car, during lunch break, etc. Just make sure to cancel the subscription if you don't want to continue.

Be realistic though, if you can learn a few phrases and all the numbers with correct tones, you'll be doing well. Have no illusions that you'll be able to "get by" in Mandarin, because you won't.

If you can quickly locate a native Chinese speaker in your area (university student perhaps?) or there is any sort of Chinese social club where they gather, then an hour or so over coffee, lunch, or dinner could help your effort considerably at little cost. Make sure person is from the north (more standard Mandarin pronunciation), and write down the phrases you most want to learn.