Because overstaying a visit can have signficant legal implications for both of you, and although this is Flytertalk, your best action is not to rely on anonymous people posting on an internet chatboard to provide accurate answers to your questions but rather, you should seek definitive information directly from CPB (as provided from CPB website):

1. You can contact the CBP Information Center (CIC) at 877-227-5511 (00+1+202-325-8000 for international callers).

Having said that, the follow FAQ https://i94.cbp.dhs.gov/I94/#/faq has the following: [emphasis added]

When I query my name in the View Compliance tab, what does days remaining in the United States mean?

The days remaining in the United Sates are the days you have left on your period of admission as listed on your current Form I-94. This number is calculated from the current day until the last day of your admission period. You must depart the United States, unless you have a pending or approved petition or application with USCIS that allowing you to remain, by 11:59 PM Eastern Time (ET) on the last day of your admission. You can find the admit until date on your current Form I-94, which is available on the “Get Most Recent I-94” tab of this website or through the CBP One™ mobile application.

Now, to me, that does not seem entirely practical for folks on the west coast and I suspect CBP actually means 11:59 PM local time. And I suspect they are authorized to use discretion for situations in which there are travel delays that are beyond the control of the visitor.

But you should contact CBP directly to find out from the horse's mouth, so to speak.