turbo, you probably know all this, but this is why I think the name of that tournament is confusing.
ASA Nationals is the championship tournament for ASA. There is one location for each age group (I don't think it's always been that way, but I believe it is this year) and there are 100+ teams competing from all over the country in each age bracket. If you win that, you would be the ASA Champion. You qualify for that tournament by winning an ASA National berth in the appropriate tournament. That's the one that is in California for 12U this year.
The ASA Eastern Nationals (and there are Western, Southern, etc.) tournament is not the championship tournament - it's one that has a separate berth system (though if you win ASA States, you win your choice of a berth to Nationals or Eastern Nationals). If you win or place in Eastern Nationals this year, you would win a berth to next year's ASA Nationals (2008), like an early bird qualifier for next season. The number of teams competing can be small. I think last year there were only nine 12U teams in Eastern Nationals (and only three teams the year before), mostly because many teams went to some Nationals the week before instead.
By the name, I think it leads people to think it may be a regional part of the current season Nationals championship tournament, but it isn't - it's just something different. Any qualification for ASA is a plus in my book, and I hope you place high and go to Nationals next year. I would just prefer they call it Eastern Pre-Qualifier or something like that.
If I got any of those details wrong, someone please correct me (do I really even have to say that?).