According to the Talmud (Megillah 16a) Achashverosh’s eunuchs rushed Haman in a state of confusion.
The Torah Temimah explains that they rushed Haman against his will to indicate the king’s lack of respect for him.
The Maamar Mordechai quotes the Yalkut Shimoni that Esther sent these servants.
Alshich writes that, aside from most of the adviser’s dislike of Haman, everyone in the palace knew that Haman was on the outs with the king, effectively blacklisting him.
In one comment, the M’nos HaLevi writes that Haman was rushed in order to not have the chance to wash off his daughter’s excrement from his head.
In another comment, he writes that if the servants had not rushed, Haman would have hanged himself.
Similarly, the Vilna Gaon writes that Haman would have used his added time to take down the gallows. Since the gallows will be needed for him, the eunuchs were rushed.
Also, Dena Pishra writes that Haman would have run to his governor sons, and they would begin the rebellion they were planning. On that note, the M’nos HaLevi points out that an opinion in the Talmud (Pesachim 22b, Kiddushin 57a) interprets any appearance of the word es to include something to a given statement. Therefore, he interprets this verse’s containing an es in “es Haman” to include Haman’s sons.
The M’nos HaLevi also notes that the word “vayavhilu” (“and they rushed”) is written without a letter yud between the hey and lamed. The missing yud has a gematria of ten, implying Haman’s ten sons.
Perhaps the fact that the addition of the ten would make the gematria of vayavhilu (6+10+2+5+10+30+6=69) the same as hadas (“willow”) (5+4+60=69) fits well with the above-cited opinion from Yalkut Shimoni that it was Esther/Hadassah who sent these eunuchs.
The Maharal explains another reason for their rushing. The organic process of nature is slow. A seed placed in the ground does not turn into a plant immediately. Anything that comes directly from H-Shem is sudden, and without preparation. The Shelah quotes from the Talmud (Brachos 9b) that kings eat their main meals in the morning. These servants are therefore rushing Haman to get to Achashverosh’s meal on time. This is the reason for his Halachic position (Shulchan Aruch Orach Chaim 695:2, Mishnah Berurah ibid., sub-paragraph 9) that a Purim seudah should ideally be held in the morning hours.
R’ Moshe Rephael Luria quotes the Midrash (Bireishis Rabba 2:4) which discusses how the second verse in the Torah (Bireishis 1:2) alludes to all four exiles of the Jewish people. The Midrash parallels that verse’s use of the word vavohu (“emptiness”) with this verse’s use of the word vayavhilu.
Another Midrash (Eicha Rabba 2:11) writes that this verse is a fulfillment of the verse from the Song at the Sea (Shemos 15:15) “az nivhalu alufei Edom” (“then the princes of Edom will tremble”). After all, Haman – a descendant of Edom – is trembling and confused from being rushed. The trembling of our enemies will come with our sudden escape from their exile, bimheira biyameinu.