Why do we commemorate the miracle on the Shabbat before Passover rather than on the tenth of Nissan, the date on which it actually took place? We see that the Torah itself mentions only the date rather than the day of the week.
It is because the miracle is closely connected to Shabbat. The Egyptians were aware that the Children of Israel observed Shabbat and did not busy themselves tending animals on that day, so when the Egyptians saw them taking lambs and binding them to their bedposts on Shabbat, they were surprised and decided to investigate what was happening.
The Children of Israel were in great danger when they were confronted and were saved only by virtue of a miracle. We therefore commemorate this miracle on Shabbat rather than on the tenth of the month of Nissan.
Moreover, had it not been Shabbat, the Children of Israel would not have needed a miracle to save them. They would have been able to deceive the Egyptians by diverting their attention or making up some kind of explanation. On Shabbat, however, they would not do so, for, as our Sages said, "Even an ignorant man will not tell lies on Shabbat." Thus, we see that they were endangered because of their observance of Shabbat, and they needed a miracle to save them.
A further reason why we recall the miracle on Shabbat rather than on the tenth of the month is that, forty years later, Miriam died on that day and the well which accompanied the Children of Israel and provided them with water in the wilderness, disappeared. When the anniversary of Miriam's death fails on a weekday, some observe it as a fast for the righteous.