I have a few issues with the Area 51 private beta invitation mail.
Q: Who can access the site during the private beta?
A: Only the 202 people who committed to it.
That's not really true. One can also sent an invite to other users that did not commit. This might be worth pointing out here already. Further, one can access the site by using the Visit link on Area 51. (Which might not be worth pointing out)
Q: How long will the private beta last?
A: Private betas generally last 1-2 weeks while you prepare the site for opening day. Once the site is populated with questions, and its initial scope established, we'll open it up for public beta.
Currently, private betas generally last 3 weeks.
Q: How long is the beta?
A: After a few months, when it becomes abundantly clear that it's Making The Internet A Better Place, we'll slap a proper logo and design on it, and make it a full-fledged citizen of the Stack Exchange network.
This usually takes longer than a few months.