E3 is coming up in a week which gives some insight into some time-line for the BETA.
Blizzard is going to most likely have a LOT to say at this E3 with Diablo3 information, the release of StarCraft2 just over a month after the convention, and of course the Cataclysm expansion.
While it might be a little too early for Blizz to promise a release date for Cata they are most certainly going to supply many clarifications and videos and new information to keep us biting. Now how does this involve the BETA?
At E3 they are most likely going to have some "Try Me" booths for the Goblin and Worgen starting zones. Usually they developer servers or a psuedo BETA server for this. With that in mind, I don't think they will begin the BETA that Tuesday so as to keep their servers clean for showing off purposes.
However, with Blizzcon so far out, closer to what we think the actual release might be, it's possible Blizz might give out some BETA keys at their panel. Giving out keys and having their voice out officially at the convention would be an opportune time for Blizz to announce the exact date of the start and wave times of key handouts of the BETA to help put to rest the malicious emails many people have received claiming to be BETA keys.
My personal prediction, with all that in mind, is that the BETA will begin no later than two weeks after E3 with the Pre-Cataclysm events Project Gnomeregan and Zalazane's Fall perhaps even starting the week of or after E3.