You must merely have your returns postmarked by the deadline. There's no impact by a failing e-filing system. Worst case, print them out, attach a check if needed and drop them in the mail.
Unless you efile after the post office closes on the night of the 18th and/or don't own a printer and/or can't get there after efile fails but before the post office closes.
Or there are people like me, where my efile was rejected on April 19th. Now what do I do? If I try to efile again, it just says, "sorry, you're past the deadline". If I mail in a form it will technically be late, although I guess if they say anything I can show them my failed efile attempt...
Also, being late isn't that bad. You'll likely get a notice in the mail detailing out any late charges. Which for being 1 day late will be extremely minor relative to your income.
And yeah, I know being late isn't terrible, and in fact if you are owed a refund there is no penalty at all. But it's still annoying that it was late because critical government run infrastructure was broken.
The main line was slow on the 18th and people had very little wait time. The 19th was much the same. There were an excess of operators who were waiting for calls on the non-specialty line.
Go read Publication 17 for guidance for next year.