Rabbi Elazar ben Azaryah says: It is stated here, "this night," and it is stated further on, "For I will pass through the land of Egypt this night" (Exodus 12:12). Just as there the meaning is until midnight, so too here the meaning is until midnight [the Pesach may be eaten only until midnight]. Rabbi Akiva said to him: But is it not stated, "and you shall eat it in haste" (Exodus 12:11), meaning up until the hour of haste [which is until dawn]? If so, what does the verse teach by saying "this night"? It comes to exclude another night. For it might enter your mind to say: since the Pesach is among the lesser holy offerings, and the peace-offering is also among the lesser holy offerings, then just as the peace-offering may be eaten for two days and one night, so too the Pesach should likewise be assigned two nights in place of two days, and it should be eaten for two nights and one day. Therefore the verse teaches us [that it is only this one night]. (If so, what does the verse teach by saying "at night"? It is to be eaten at night and is not eaten by day.)
Until Midnight or All Night the Dispute Over Eating the Pesach
Yalkut Shimoni on Torah 197:4
רַבִּי אֶלְעָזָר בֶּן עֲזַרְיָה אוֹמֵר, נֶאֱמַר כַּאן בַּלַּיְלָה הַזֶּה, וְנֶאֱמַר לְהַלָּן (להלן פסוק יב) "וְעָבַרְתִּי בְאֶרֶץ מִצְרַיִם בַּלַּיְלָה הַזֶּה", מָה לְהַלָּן עַד חֲצוֹת אַף כָּאן עַד חֲצוֹת. אָמַר לוֹ רַבִּי עֲקִיבָא, וַהֲלֹא נֶאֱמַר "וַאֲכַלְתֶּם אֹתוֹ בְּחִפָּזוֹן", עַד שְׁעַת חִפָּזוֹן, אִם כֵּן מַה תַּלְמוּד לוֹמַר בַּלַּיְלָה הַזֶּה, לַמְּעוּטֵי לַיְלָה אַחֵר, סַלְקָא דַּעְתָּךְ אֲמִינָא הוֹאִיל וּפֶסַח קָדָשִׁים קַלִּים וּשְׁלָמִים קָדָשִׁים קַלִּים מָה שְׁלָמִים נֶאֱכָלִין לִשְנֵי יָמִים וְלַיְלָה אֶחָד אַף פֶּסַח נַמִּי אוּקִי שְׁנֵי לֵילוֹת בִּמְקוֹם שְׁנֵי יָמִים וִיהֵא נֶאֱכָל לִשְנֵי לֵילוֹת וְיוֹם אֶחָד, קָא מַשְׁמָע לָן. (א"כ מַה תַּלְמוּד לוֹמַר בַּלַּיְלָה בַלָּיְלָה הוּא נֶאֱכָל וְאֵינוֹ נֶאֱכָל בַּיּוֹם).