I can clarify that the beta is not 2 weeks long. The beta did start on the 17th for Playstation owners and is now down for maintenance for the next 2 days. It will resume on the 23rd and allow Xbox owners to join and it will end on the 27th.
You will have plenty of time to experience what this Beta has to offer. I started late (the 19th) and having only logged a little more than six hours play time, I had managed to reach the Beta lvl cap of 8, completed all the available story, ran the fire team strike mission, did a bit of the exploration and dabbled in The Crucible PvP. I am by no means trying to sound boastful, just giving you an idea of how much time you will have to enjoy the Beta. Have fun! =)
It is definitely enough time. With how much content is in the game right now, you can finish it in 2 days and have time to spare. I spent half of the first day of the PS beta downloading and I was done with everything by the end of the next day.