The mishna teaches that the Pesach offering may be eaten only at night
and only until midnight. To whom is this attributed? The g'mara says
that it was Rabbi Eleazar ben Azariah who taught this, based on these
two passages in torah: "they shall eat the flesh in the night" and also
"I shall go through the land of Egypt that night" (to slay the first-born).
Since the latter ended at midnight, so too must the former. Rabbi Akiva
questioned this, saying that it says "you shall eat it in haste" -- which
means you have until morning because that was the "time of haste"
(when Israel fled). The g'mara does not hold by R. Akiva. (57b)
The seder, which replaced the Pesach offering, is supposed to end by midnight.
(I gather that it is also meritorious to go until midnight -- so we
can tell the story thoroughly -- but could be misunderstanding.) This is
midnight by division of hours -- halfway between sunset and sunrise -- not
midnight by the clock. (That time of year around here, midnight is close to
1:30AM.)