The Korban Pesach is meant to commemorate the miracle of the Jewish households being “passed over” in Egypt.
But why were they ever at risk? The other plagues were punishments to the Egyptians for enslaving the Jews. If the plagues were targeted, why should there have been any threat to the lives of the Jewish firstborn, to the extent that we celebrate that they were spared?
no special “sign” had to be made to G-d that He should leave them be, and no special sign is remembered today. So why is the salvation of the Jewish firstborn different, so much so that it required demonstrable acts that they were Jews by spreading blood on their doors, and later generations then had to remember this act by eating the Korban Pesach?
R’ Yitzchak Blaser explains that the Gemara in Yuma 86a teaches that even though repentance alone does not usually atone for a violation of a negative commandment; nevertheless, on Yom Kippur the flood of mercy is so great that if a person repents, he can have achieve forgiveness – even if they might not deserve it!
The Midrash says: Woe to the wicked, who convert Divine mercy to strict justice (מדת הדין into מדת הרחמים).
R’ Yitzchak Blaser explains that what the Midrash means is that if a person had an opportunity to erase sins they couldn’t get rid of an entire year, and turned their back on this opportunity, the disdain for the mercy shown rebounds, and it becomes strict justice.
Although the Jews had served the Egyptian idols, it hadn’t been out of choice. But with the Exodus over, and Hashem having saved them, they had the chance to throw off any trace of idol worship and show their commitment and dedication to Him by taking a lamb, an Egyptian deity, and in their faces, roast it, eat, and put it’s blood on display.
If they turned their backs on this ideal opportunity they would have incurred Hashem’s wrath and מדת הדין.
The other plagues were specific punishments that the Jews were not deserving of, but the 10th plague was not “just” a punishment for the Egyptians, unlike the previous plagues, as it had a secondary function. Whilst all the plagues were punishments in that they revealed Hashem’s hand in nature to the Egyptians, the Jews were not meant to be punished in this way. But here they had an opportunity to throw off the yoke of idol worship, and had they not used this opportunity, they would have incurred a מדת הדין, and the Korban Pesach we take is a remembrance of the kindness we were shown, that led to us being saved.
This explains why the Mechilta says that the Jews were as deserving of destruction in the final plague as the Egyptians, up until the final Korban Pesach was brought.
Also, in Pirkei d’R’ Eliezer, it says that some people would not undertake circumcision, the merit of which was needed for the גאולה as well (דם פסח ודם מילה). So Hashem told Moshe to make the Korban Pesach, and Hashem sent a breeze from Gan Eden, which caused people to faint at the irresistible aroma, at which point Moshe said כל הערל לא יאוכל , and they immediately underwent circumcision.
All this shows Hashem’s great mercy, as the Targum translates ופסחתי (Shemos 14:13) as a word meaning “compassion”.