What is the basis for the idiomatic understanding of "three days in the tomb" as two nights and a day? The Messiah said that He would be three days and three nights in the "heart of the earth"  
There are those who think that the crucifixion took place on the 6th day of the week with the resurrection taking place on the 1st day of the week.
Of those, there are some who think that the "heart of the earth" is referring to the tomb.
A 6th day of the week crucifixion/1st day of the week resurrection allows for only 2 nights to be involved. 
To account for the lack of a 3rd night, some of those mentioned above say that the Messiah was employing a common figure of speech/colloquial language. 


I wonder if anyone who thinks that it was common could provide examples to support that belief; i.e., instances where a daytime or a night time was forecast or said to be involved with an event when no part of the daytime and/or no part of the night time could have occurred.
Unfortunately I can't find the original source (yet), but according to this commentator, the Jerusalem Talmud states that a portion of a day was as a whole.


  The Jerusalem Talmud quotes rabbi Eleazar ben Azariah, who lived around A.D. 100, as saying: “A day and night are an Onah [‘a portion of time’] and the portion of an Onah is as the whole of it” (from Jerusalem Talmud: Shabbath ix. 3, as quoted in Hoehner, 1974, pp. 248-249, bracketed comment in orig.). 


The Jerusalem Talmud is also known as the Palestinian Talmud.

PS As the answer to the OP question, the reference (the argument amongst the early sages like Eleazar ben Azariah) is to the command "be ready on the 3rd day" (Ex. 19:15) with day defined earlier in Gen. 1:5, 8 (dark/evening and light/morning).  So, some sages thought in terms of periods (dark or light) to make a day.  When is the third day?  Some thought at least 4 periods, some 5, some 6 (Ishmael).  One said always 5 (Aqiva).  Following are examples.

4 PERIODS

before sunset (1 period and day 1)

night, morning (2 periods (or 3 total) and day 2)

night (1 period (or 4 total) and day 3)

5 PERIODS

night, morning (2 periods and day 1)

night, morning (2 periods (4 total periods) and day 2)

after sunset (1 period (5 total) and day 3)

6 PERIODS

night, morning (2 periods and day 1)

night, morning (2 periods (4 total) and day 2)

night, morning (2 periods (6 total) and day 3)

So, traditional Christianity counts the sign of Jonah as 4 periods to mean 3 days (Fri-Sun).

Some count the full 6 periods (3 days and 3 nights) in ways like Thursday after sunset to Sabbath at sunset.

What is totally wrong is the newish theory of death on Wednesday to either resurrection at Saturday sunset (7 periods or 4 days) or Wednesday to Sunday resurrection (9 periods or 5 days).