Rabbi Tzvi Hirsh Horowitz writes that, on the simple level, it is easy to see that Haman, being the constantly conniving, calculating political creature he is, Haman intentionally does not want to specify which nation he intends to destroy because he is concerned that the king or new queen might harbor positive feelings for the Jews. After all, it is poor form to suggest the destruction of a nation for whom the king has a positive bias.
The Ginzei Melech writes that Haman is asserting that the Jews consider themselves an “am echad” (“one nation”) – a united front – even against those greater than them. In other words, the Jews as a unit disrespected Mordechai in attending Achashverosh’s party. Thereby, they weakened Mordechai’s ability to influence them, and therefore put themselves at risk. In Haman’s estimation, this is a weakness he can exploit to the Jews’ detriment. This feeling that all Jews are equal goes along well with the famous exchange between President Harry Truman and the first president of the State of Israel, Chaim Weizmann. When Truman complained that he was “the President of so many millions of Americans,” Weizmann replied that his own job was harder since he was “the President of a million presidents!” As a people, Jews can be hard to lead since they consider themselves united, even against authority.
Of course, everything Haman said in the negative about the Jews has a positive side he is intentionally ignoring. After all, as Rav Samson Raphael Hirsch writes (Collected Writings, Volume II, 385-6) “The Jewish nation, however [in contrast to other nations (see Koheles 5:8)], exiled throughout the world, uniquely maintains its identity, remains a stranger among the nations and is unable to be fully absorbed.” Being an “am echad,” the Jews retain their individual nationality, allowing them to better influence the world.