Heh, I don't often realize that I might be living some people's dream... I'm not an archaeologist, but that's only because I dig up live people instead of dead ones (a.k.a. anthropology).
It can be a pretty cool line of work, though, especially if people are willing to pay you to do it.
About Earthwatch: I'd think that it would be a lot easier (and cheaper) to contact a local anthropology/archaeology department (they're the same thing at most universities) in the summer and ask if they are running any field schools... and ask if you can just tag along. They're always dying to have help, especially if you are willing to be a shovel bum.
My advisor does Icelandic archaeology up here every other summer, and they haul along all kinds of shovel bums to do the gruntwork (digging and sorting/sieving). It's better working up in this kind of weather (cool, in the 50s on a nice day) than in the hot summer sun where most of the archaeologists do their work! So come to Iceland for a couple weeks this summer if you want to help dig up Viking longhouses (all you need to do is pay for your airfare, food, and a tent).