Washington Post has reported that Direct Deposit payments start on April 9th, next Thursday (which makes some sense, as I believe that the IRS makes it's payments on Tuesdays and Thursdays).
Now there's two slightly different dates given:
The IRS says that payments start on the 9th and folks that do direct deposit will get it on or near (depending on how fast your bank processes stuff) April 9th, with the latest being April 14th.
The Treasury Dept made another statement saying released on the 9th, but most would get it (if using direct deposit) no later than April 17th.
In sum, it looks like the wide range of dates is to account for people's different banking situations. For example, if someone decides to sign up through the IRS' new direct deposit sign up website, it will take more time for them to verify that it is in fact you who is the owner of the account, and not some fraud scheme. This is typical, as with making electronic transfers (whether to receive direct deposit from your job, or just to transfer to someone else's account) it usually take a few days for everything to be verified (again, this is for very necessary safety reasons). This is doubly so if you are using a pre-paid debit card like through Netspend or something- they want to check that you are the account holder. As such, you won't get your money right away.
So if you are someone who just signed up for direct deposit, and the IRS has never made a direct deposit to you before, the time to verify you means you'll get it probably between April 13th through April 17th. Seeing as how the IRS allegedly releases stuff on Tuesdays and Thursdays, you'll get it in your account on either April 14th or April 16th.
If the IRS already has your banking info, and they have made a direct deposit to you before, you'll get it in your account either April 9th, or April 14th. Maybe the 16th if you're unlucky.
So next week or a little beyond that for most of us. Hope this helps put some folks here at ease.