It will work even though Turbo Tax says May 17. I'm in Texas, too, and I e-filed today, a few minutes ago (Monday, June 14). The IRS will know you're from Texas and recognize the June 15th extension.
The only catch is you cannot specify a later date for your payment if you owe taxes. In that respect, Turbo Tax doesn't acknowledge the Texas extension, and thinks you're filing late. Because of that, TT does not allow you to specify a debit date later than the day you file.
