I think the primary factor is that the scripture plainly states that he was crucified on the day of preparation (Friday the 15th). Preparation for the Sabbath that is - not the Passover. It was a capital offense to work on the Sabbath, so all the work had to be done the day before - preparation!
Mark 15:42 (KJV)
And now when the even was come, because it was the
preparation, that is, the
day before the sabbath,
Luke 23:54 (KJV)
And that day was the
preparation, and
the sabbath drew on.
John 19:31 (KJV)
The Jews therefore, because it was the
preparation, that the bodies should not remain upon the cross
on the sabbath day, (for that sabbath day was an high day,) besought Pilate that their legs might be broken, and that they might be taken away.
The body had to be taken down from the cross before Sundown - which was the beginning of Saturday or the Sabbath. The day of crucifixion (Friday the 15th) was counted as the first day of the three; Saturday was also a full day, and Sunday was rounded up as a full day. Their time measurment was rather course, so I wouldn't want to get too hyper-literal about the three days. Technically, the translators should have said - "He was in the tomb one full day, four watches, and six hours." Rounding up to three days makes it simple.
The first Passover happened on the selfsame day of April 14th 1462 BC, the next day Moses left Egypt with 600,000 footmen and families. The same day as the Lord led the slaves of sin out of bondage. Wonderful parallel.
Larry