The Yerushalmi (mentioned in yesterday’s post) writes that the simcha of Purim established by Sanhedrin cannot be celebrated simultaneously with the simcha of Shabbos, which was established by G-d, and therefore if Purim falls on Shabbos, the seudah is pushed off until Sunday. The Bavli does not mention such an idea; whether that silence indicates disagreement or not is a subject of major debate. The Ran already is uncomfortable with the whole idea of celebrating seudas Purim on the 16th when the megillah explicitly tells us “lo ya’avor”, that the date of the celebration cannot extend beyond the 15th. Another problematic element of the Yerushalmi is the assumption that Shabbos is not just a day of oneg, but includes an obligation of simcha as well. Tosfos in M.K. (23b d”h “man”) writes that the reason a Yom Tov cancels aveilus and Shabbos does not (i.e. if a Yom Tov falls out in the middle of shloshim or shiva, one does not resume mouring after Y”T) is because Y”T is a time of simcha and Shabbos is not. Even if one grants the assumption that Shabbos is a day of simcha, whether we apply this idea of “ain m’arvin simcha b’simcha”, not celebrating two simchas simultaneously, to this type of simcha is debatable (see M”K 8). No one would suggest, for example, that a pidyon haben needs to be rescheduled until after chol hamoed so as to not mix the two elements of simcha.
Is there any explicit gemara in the Bavli that we can point to as being in disagreement with the Yerushalmi? The Bavli (Meg 30a) quotes an argument between Rav and Shmuel when to read parshas zachor in a year such as this one where Purim falls on a Friday. Rav says to read zachor the week before Purim, as we do, so that the reading precedes the Purim. Shmuel, however, argues, and says zachor should be read on the Shabbos of the 15th so that “zechira v’asyia b’hadei hadadei”, the reading of zachor and the celebration of Purim for those in walled cities will be simultaneous. The simple reading of the gemara clearly implies according to Shmuel that the celebration of Purim is not pushed off until Sunday, but occurs on Shabbos itself, the same day that zachor is read. The Pri Chadash and others attempt to refute this proof, but certainly at first glance it seems very convincing.
For those with a hearty appetite, it probably is not such a big deal to make a seudah on Shabbos and a seudah on Sunday to be yotzei all opinions. However, you still can’t completely escape the debate, because one must decide on which day(s) to say “Al haNissim”. For those with a hearty appetite for learning and want a fuller treatment of this topic, R’ Ovadya Yosef in the first volume of Yechaveh Da’at has a nice review of the issues involved in a "Purim meshulash".