I've heard 2 weeks so far, and the Halo Reach beta lasted longer than that(17 days wasn't that long, but I'm hoping this Beta will be at least a month's worth), so I'm expecting up till the beginning of August or halfway through August myself. The Beta Date update doesn't say how long it lasts either, I need confirmation.
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My guess is PS4 owners will get it for a month and XB1 owners will get it for half that.