In Jewish communal life part of a day is at times reckoned as one day; e.g., the day of the funeral, even when the latter takes place late in the afternoon, is counted as the first of the seven days of mourning, a short time in the morning of the seventh day is counted as the seventh day; circumcision takes place on the eighth day, even though of the first day only a few minutes remained after the birth of the child, these being counted as one day.
Again, a man who hears of a vow made by his wife or his daughter, and desires to cancel the vow, must do so on the same day on which he hears of it, as otherwise the protest has no effect; even if the hearing takes place a little time before night, the annulment must be done within that little time.
The day is reckoned from evening to evening—i.e., night and day—except in reference to sacrifices, where daytime and the night following constitute one day (Lev. vii. 15; see Calendar).
(Jewish Encyclopedia/ Day)
Augustine says (De Trin. iv): "There were thirty-six hours from the evening of His burial to the dawn of the resurrection, that is, a whole night with a whole day, and a whole night." (Catholic Encycloprdia/ Summa Theologica > Third Part > Question 51)
Jesus said he would be in the heart of the earth for three days and three nights. (Matthew 12:40)
Now the question becomes does God reckon time by Jewish idioms or by Catholic doctrine? If so then he must abide by man's reckoning with regard to parts of three days or the Catholic doctrine of thirty-six hours.
On the other hand, what if we take Jesus' words literally with regard to the sign of Jonah?
The expression "three days" occurs 61 times in the KJV. The expression "three days and three night" occurs 3 times in the KJV.
Jesus could have said he would be in the earth three days, but he didn't. Jesus was much more specific. Why? Was it because he would be entombed for a specific period of time or was he entombed for an undefined period of time according to Jewish idioms?
The problem with the part of a day theory and the Catholic thirty-six hour theory is that neither allows for two Sabbaths.
Now when the Sabbath was past, Mary Magdalene, Mary the mother of James and Salome bought spices that they might come and anoint Him. (Mark 16:1 NKJV)
What Sabbath?
Therefore, because it was the Preparation Day, that the bodies should not remain on the cross on the Sabbath (for that Sabbath was a high day), the Jews asked Pilate that their legs might be broken and that they might be taken away. (John 19:31 NKJV)
That Sabbath was a High Day, an annual Sabbath.
So when the annual Sabbath passed the women bought spices so that they might anoint the body. Then they returned and prepared spices and fragrant oils. And they rested on the Sabbath according to the commandment. (Luke 23:56 NKJV)
After the annual Sabbath the women bought spices, prepared their spices and then rested on the weekly Sabbath.
There were two Sabbaths which doesn't fit within a Jewish three day idiom or the Catholics' thirty-six hour theory.
Why can't the sign of Jonah be true? Jesus' sign allows for the two Sabbaths.