Suppose Moshiach arrives between Pesach and Pesach Sheni - would we bring a Korban Pesach on Pesach Sheni as we did not bring one for Pesach or was there no Chiyuv in the first place and we would not bring one for Pesach Sheni? (sources please)
A majority of Jews cannot bring a Pesach on Pesach Sheni. Only a minority can, and only if the majority brought theirs on Pesach Rishon. Pesachim (79a-80b).
In a translation of a talk by the Lubavitcher Rebbe from Shabbos Parshas Emor 5738 (1978), the Rebbe brings that most opinions hold that the Jews will be obligate to bring the Pesach Sheni, and points to the Minchas Chinuch. emphasis mine:
The original Pesach Sheni was instituted for those who were unclean or could not otherwise offer the Pesach sacrifice in its proper time. The proper observance of Pesach renders Pesach Sheni unnecessary. What reason, then, is there for a Jew who has celebrated Pesach properly to commemorate Pesach Sheni?
A Jew constantly yearns for and awaits Moshiach's coming, when the Beis HaMikdosh will be rebuilt. Should the Beis HaMikdosh be rebuilt in the period between Pesach and Pesach Sheni, the Jewish people will be required to bring the Pesach offering on Pesach Sheni. [According to most opinions. See Minchas Chinuch, Mitzvah 380.] The expectation of the imminent arrival of Moshiach obligates a Jew, immediately after Pesach, to begin preparations for Pesach Sheni. And, even if Moshiach has not come by Pesach Sheni, it is proper to at least commemorate Pesach Sheni.
The Relevant Minchas Chinuch is here (first column, 18 lines down). He says that the whole idea of looking whether the majority or minority of people missed the first Pesach (majority - don't do Pesach Sheni ;; minority - do Pesach Sheni -- see @Barrry's answer) is a divine decree and only applies if one is able to do the first Pesach offering. It is therefore clear that if Moshiach comes between the first and second Pesach, everyone becomes comparable to a convert and does bring the Pesach Sheni.
The Minchas Chinuch concludes (and it is apropos), "I write this between the first and second Pesach, may it be G-d's Will that the Temple will be speedily rebuilt before Pesach Sheni, and we will merit and bring the second Pesach offering, Amen and Amen."
In a talk from the last day of Pesach, 1968 (published in Likkutei Sichos, Vol. XII, pp. 216-220), the Rebbe discusses the argument in the Talmud Yerushalmi concerning the Pesach Sheni if the Beit Hamikdash is rebuilt between the first and second Pesach, and explains how it is not arguing with the statement of the Talmud Bavli (Pesachim 80A) that if a majority of people did not bring the first Pesach, they would not bring the second Pesach.
Rav Eliyashiv(v'yishma Moshe) answered that it is a machlokes in the Yerushalmi pesachim 9:1 and lamaaseh we would bring it.see שו"ת יוסף אומץ סימן ו.
Here is an answer from the Lubavitcher Rebbe Zatzal