Haman's potential for destroying the Jewish people was hinted at in his own description of the nation: "There is a people that is dispersed and divided..." [Esther 3:8]. It is only because there is division and unjustified hatred within the Jewish nation that their enemies have the ability to harm them.
When the Jews are divided, they represent only individuals -- not a Klal [a communal entity]. When that happens we have lost our strength.
Haman's whole plot was based on the division of the nation. That is why G-d insisted that each Jew should give exactly one half shekel. The symbolism of the half shekel is that each Jew is only a fraction of the entity. He needs to combine with his fellow Jew to make a significant contribution. If we think we can be 'an entire shekel unto ourselves', that is not going to work. Our strength is through the recognition that we need each other, and the realization that we need to set aside our petty differences to come together to provide a complete shekel.
This is the strength that ultimately saved the Jewish people. Because of the terrible calamity that was hanging over them as a result of Haman's decree, they decided to put away those 'dispersions and divisions in the nation' and came together as a unit and as a whole.
Based on Rabbi Frand who once heard this interpretation of this Gemarah in the name of the Yismach Yisrael.