(a) The Gemara in Megilah (29b) explains that we begin to be "Sho'el
v'Doresh b'Inyano Shel Chag Sheloshim Yom li'Fnei ha'Chag" -- we expound in
public the Halachos of the festival *thirty days* before the festival
begins. We see from there that the period of preparation for an event is
thirty days. Similarly, the Gemara in Megilah explains, in preparation for
buying the Korbanos Tzibur on the first of Nisan the announcement about the
collection of Shekalim is made thirty days in advance.
The Gemara in Megilah cites another opinion, that of Raban Shimon ben
Gamliel, who maintains that we expound the Halachos of the festival only
fourteen days (two weeks) before the festival. We see, then, that according
to Raban Shimon ben Gamliel, the time period of preparation is fourteen
days, and not thirty days. The Gemara in Megilah explains that according to
his opinion, they would announce the collection on the first of Adar because
that is fourteen days before the fifteenth of Adar, which is the day which
the collection begins in full earnest, the day on which the money-changers
began to operate (and Beis Din begins taking collateral from people who did
not yet give the half-Shekel).
(b) RABEINU MESHULAM suggests an original explanation. The Gemara (Ta'anis
7a) says that it takes fifteen days to travel from Yerushalayim to the
farthest point in Eretz Yisrael. The announcement made on the first of Adar
was to announce the collection of the Shekalim from the residents of Eretz
Yisrael (the announcement for those who lived outside of Eretz Yisrael was
made earlier, according to one opinion in the Gemara). The Beis Din in
Yerushalayim makes the announcement, says Rabeinu Meshulam, and sends out
messengers to inform all of the towns in Eretz Yisrael. It takes them
fifteen days to arrive at the farthest places, and it takes another fifteen
days for the Shekalim to arrive in Yerushalayim from those places. Therefore
the announcement is made at the beginning of Adar.
The Gemara Bavli (in Megilah), which gives a different reason for the
announcement being on the first of Adar, perhaps holds that the Shekalim may
arrive later than the first of Nisan (in accordance with the other opinion
in the Gemara here at the end of this Amud). The Gemara Yerushalmi, though,
holds that all of the Shekalim must be collected by the time Nisan arrives,
and therefore Rabeinu Meshulam is justified in suggesting that the reason
for the announcement is simply to make sure that they arrive on time.
(c) The Gemara in Megilah (13b) gives another reason why the Shekalim were
collected at the beginning of Adar. The Gemara says that Hashem commanded
the Jewish people in the Midbar to give a half-Shekel, because it was known
to Hashem that many generations later, the wicked Haman would give a large
sum of Shekalim to Achashverosh for the rights to destroy the Jews. The sum
of Shekalim that Haman would give would correspond to the total amount of
Shekalim that the Jews gave when they were first commanded to give Shekalim
in the Midbar. By commanding them to give Shekalim, Hashem prepared the cure
before the illness, for in the merit of their Shekalim, the Shekalim of
Haman were ineffective. Therefore, the Rabanan enacted that each year, the
half-Shekel should be given before the time of Haman's lots (which were done
on the thirteenth of Adar).
Why, though, did they enact that it be given *two weeks* before that time?
The VILNA GA'ON (Mishnas Eliyahu) explains that the Midrash says that Haman
rejoiced that his lots fell out on Adar, the Mazal of which is Dagim
(Pisces). Haman viewed this as a bad omen for the Jews, for fish swallow
each other, and thus the whole month had an ominous proclivity for the
Jewish people. Therefore, the Shekalim are given at the beginning of Adar in
order to arouse Hashem's mercy to make the Mazal of Adar be an auspicious
one for the Jews (so that their *enemies* would be swallowed up like fish).