The issue is that TurboTax doesn't file the tax return for you - that is not a full service provider.
What they do - the provide the software and and the gateway for you to file.
That means - it is your responsibility to verify if your tax return went through.
Generally what you need to verify - there should be conformation e-mail that your tax return was accepted by the IRS - and that step is very important.
Normally you woudl receive such email as a matter of a couple of minutes - but as you filed at the last day - that might take longer.
If your email is lost or overlooked - TurboTax provides this page to verify the status
If neither works or you have doubts - you may order the tax return transcript from the IRS or you may verify by calling the IRS _1_800_829_1954_ and get an update.
If you did receive a confirmation email but the tax return was NOT actually accepted by the IRS - that woudl be an issue with TurboTax as an e-file provider - and you might have a case.
Here is how to contact TurboTax support
Sorry for your situation.
In your current situation - I suggest to mail your tax return to the IRS.
Let me know in which state
you live - and I will verify correct mailing address.
If you do not have any outstanding tax liability
- there should not be any penalty.
Any questions? Just Ask!