The deadline is hard-wired in the US Code at 26 USC 6072
(a) General rule. In the case of returns under section 6012, 6013, or
6017 (relating to income tax under subtitle A), returns made on the
basis of the calendar year shall be filed on or before the 15th day of
April following the close of the calendar year and returns made on the
basis of a fiscal year shall be filed on or before the 15th day of the
fourth month following the close of the fiscal year, except as
otherwise provided in the following subsections of this section.
It is interesting to note that 26 USC 6071 says
(a) General rule: When not otherwise provided for by this title, the
Secretary shall by regulations prescribe the time for filing any
return, statement, or other document required by this title or by
This section grants the Sec'y. the power to regulatorily set the filing time, when not otherwise provided. But §6072 seems to be exactly proving otherwise. In fact, taxes should have been due on the 15th, period, who cares about weekends and holidays? Congress did: 26 USC 7503
When the last day prescribed under authority of the internal revenue
laws for performing any act falls on Saturday, Sunday, or a legal
holiday, the performance of such act shall be considered timely if it
is performed on the next succeeding day which is not a Saturday,
Sunday, or a legal holiday.
There are other provisions in Ch. 77 allowing the deadline to be kicked down the road, such as in response to a federally declared disaster. There are "otherwise" provisions in the title, and I found none that pertain to computer screwups. (I must confess that I did not real the entirety of Title 26).
The evidence that the deadline has been extended is circumstantial, perhaps being an impromptu decision at a rally by the Sec'y (there does not seem to be any piece of official paper out there). It is entirely possible that he exceeded his authority, and it is entirely inconceivable that anyone will get an emergency court order enforcing the statutory deadline.