Unfortunately there is no way to get any more information. You basically just have to wait. Check Get My Payment on the IRS web site once a week or so. It might change.
TurboTax does not get any information from the IRS about your stimulus payment. What TurboTax says is just an assumption about how the IRS will process the payments. That assumption might or might not be correct for your particular case.
The whole stimulus payment system was thrown together in a big rush, and it has a lot of rough edges.
