It took a lot more prep work, usually a month (and still does even without a sacrifice) to prepare because of the limited amount of time one had between the time of slaughter, the fact that all sacrifices had to be done in one place by an entire nation in one spot, and that everyone had to dine before a specific moment.
The historian Josephus records contemporary Passover celebrations in which he estimates that the participants who gathered in Jerusalem to perform the sacrifice in the year 65 CE were “not less than three million” (Josephus, Wars, 2:280). The Talmud (Pesachim 64b) similarly records:
King Agrippa once wished to take a census of the hosts of Israel. He said to the high priest, “Cast your eyes on the Passover offerings.” He took a kidney from each, and 600,000 pairs of kidneys were found there, twice as many as those who departed from Egypt, excluding those who were unclean and those who were on a distant journey, and there was not a single paschal lamb for which more than ten people had not registered; and they called it: “The Passover of the dense throngs.”--The Paschal Sacrifice (Korban Pesach), My Jewish Learning.
The sacrifice of each lamb was divided among a set of three (3) Jewish laypersons in order for it to work and take the lamb home, and it would be even more vital and far more difficult to do if the Passover fell on a literal Sabbath, limiting what a layperson could and could not do:
The people taking part in the sacrifice were divided into three groups. The first of these filled the court of the Temple, so that the gates had to be closed, and while they were killing and offering their Passover lambs the Levites on the platform (dukhan) recited the Hallel (Psalms 113-118), accompanied by instruments of brass. If the Levites finished their recitation before the priests had completed the sacrifice, they repeated the Hallel, although it never happened that they had to repeat it twice. As soon as the first group had offered their sacrifice, the gates were opened to let them out, and their places were taken by the second and third groups successively.
All three groups offered their sacrifice in the manner described, while the Hallel was recited; but the third group was so small that it had always finished before the Levites reached Psalm 116. It was called the "group of the lazy" because it came last....When the sacrifice was completed and the animal was ready for roasting, each one present carried his lamb home, except when the eve of the Passover fell on a Sabbath, in which case it might not be taken away. If the 14th of Nissan fell on the Sabbath, the first group stationed itself on the mount of the Temple in Jerusalem, the second group in the ḥel, the space between the Temple wall and the Temple hall, while the third group remained in the Temple court, thus awaiting the evening, when they took their lambs home and roasted them on a spit of pomegranate-wood, On all other days, they could do it before nightfall (and if the 15th of Nissan fell to be on the Sabbath they would have to).--Passover Sacrifice: The Three Groups of Lay People/The Home Ceremony--Wikipedia.