What time is the latest time that Turbo Tax will allow you to submit your return on April 15th?

You can transmit your return anytime up until midnight on April 15th.  After that it won't be April 15th anymore.  You can still transmit (submit) your return after April 15th.  But if you do s0 after the 15th the IRS will consider it late, unless you file an extension.  If you do file your return late and you don't owe any tax there won't be any penalty.  

OF course, if you and thousands of others push the deadline, you all might crash whatever server you are filing through, or it might simply get delayed by their servers throttling their load.  Then, you can point fingers all you want, but the IRS doesn't care who is at fault...late is late.

Don't push it.