According to the Malbim, by saying the next party will be “according to the word of the king,” Esther was implying that her only motivation in making a request of the king is that the king, himself, asked her to do so in the previous verses.
R’ Elisha Galico says Esther was stroking the king’s ego by implying that only Achashverosh could give Esther what she wanted.
Rashi writes that Esther was suggesting that she was going to finally acquiesce in revealing the secret of her ancestry, which Achashverosh has been asking her for years (see Esther 2:10).
According to Rebbetzin Tzipporah Heller, Esther planned for the next party to specifically occur the next day in order to “intensify the effect of her plan.” This would make the tension between Achashverosh and Haman more palpable.
According to Rav Dovid Feinstein, this immediacy of the next party would pique Achashverosh’s curiosity, and keep him in suspense. Besides this, it is important to remember that the Jews were already fasting for two straight days, and Esther had asked the Jews to fast for three days, culminating in the next day. The merit of their fasting will both spiritually and psychologically support Esther’s efforts at that day’s feast.
According to R’ Meir Arama, pushing the next party into the next day was Esther’s attempt to stall her inevitable request from the king. Without a clear sign from H-Shem, she was confused if she should fight Amalek using Yaakov’s method, or Moshe’s. Yaakov (Bireishis 32:9) attempted to defeat Eisav, Amalek’s ancestor, through gifts. Moshe (Shemos 17:8-13) utilized prayer and war against the nation of Amalek.
The Yalkut Shimoni (1056) writes that Amalek is defeated machar, tomorrow. This is because Moshe, at the first national encounter against Amalek, said “tomorrow I will stand on top of the mountain” (Shemos 17:9).
The Maharal explains that Amalek does not recognize an other, a tomorrow. Amalek causes religious doubt (the Hebrew word safek has the same gematria as Amalek.) by forcing the brain to consider only one approach to a Torah dilemma; if that approach does not work, there can be no other way to look at the topic.
Perhaps another reason why the next day was so critical to Esther’s plan can be gleaned from the gematria of the Hebrew word machar, (“tomorrow”) (40+8+200=248). This is the same number as the positive commandments (Makkos 23b-24a), which themselves correspond to the major bones and sinews in a man1. Therefore, one more day of the Jews performing positive mitzvos and teshuva will help Esther. Perhaps this is the reason why the Midrash later notes that Haman was advised to approach Achashverosh specifically baboker (“in the morning”) (Esther 5:14), which the Midrash says is the time of reading the Shema.
1The significance of this number is also the reason for adding three words to the twice daily recitation of the Shema, which would only have 245 words alone (see Shulchan Aruch Orach Chaim 61:3 and Mishnah Berurah 61:6).