Efiling has nothing to do with TurboTax Support's business hours. You can efile even when Support is closed.
By the way, Support will have extended hours today. 5AM-9PM Pacific (8AM-12 Midnight Eastern).
The IRS deadline for efiling today October 15 is midnight your local time (actually to be safe it's likely 11:59 PM).
If you efile today, and find out that the efiled return was rejected for some reason, you will have until October 20 to correct the return and either resubmit the efile or to print and mail the return.
