I'm not sure about this rugby scrum origin theory.
I found a snippet of a 1981 William Safire column in New York Times Magazine article that indicates this guess was put forth by an AJ Gracia of Southbury, Connecticut.
It goes on to call it an "offbeat etymology." Etymonline has the phrase dated from 1958, but with no mention of rugby.
I found the phrase used over a decade earlier ( 1947 ) in the English translation of Haitian Jacques Romain's Masters of the Dew done by Langston Hughes and Mercer Cook.
Again, no rugby context: It would be interesting to know what original French phrase was translated as such.
Hughes went on to use the phrase again in Simple Takes a Wife , 1953—the
next reference I can find in print.
Edit :
Safire wrote another column on the phrase in 1997 which drops the mention of rugby altogether.
He concludes "a black-English origin for the phrase is pretty likely" and cites a 1954 example, four years earlier than OED 's earliest reference (1958).
He also dug up this more plausible origin of the phrase: Other evidence there of the phrase's black origin is a recollection from Norman Pierce of Jack's Record Cellar in San Francisco of Shove Day, or Bump Day, the traditional Thursday off for domestic servants in the 1920's, ''on which blacks 'accidentally' jostled whites in public places, railways, streetcars, etc.''
Edit #2 :
I just found another antedating of the phrase.
These are from Black Thunder by Arna Wendell Bontemps (close friend of Langston Hughes), 1936:
english.stackexchange.com/users/5822/Callithumpian
Answers.com also cites the rugby reference.
It also notes the other meaning of the phrase as in "They supposedly support equality, but when push comes to shove they always seem to promote a man instead of a woman".
I think the difference is "if" vs. "when".
I see think the "when" meaning is more prevalent.
It means "when actually tested".
english.stackexchange.com/users/3436/David W
Push is just a push, and things have escalated to a shove now.
It now means business.
Escalate to get the thing accomplished.
english.stackexchange.com/users/9982/mlcblog
According to this site , this term comes from rugby, where, after an infraction of rules, forwards from each team face off and push against one another.
english.stackexchange.com/users/1446/Anderson Silva
Well my understanding of the phrase has always been this: Pushing and shoving is a way of referring to fighting, particular little man-to-man arguments.
They start with a push and a shove, so when "push comes to shove", it means a fight will break out.
Fighting is the last resort, or at least the least desired outcome of an argument.
english.stackexchange.com/users/2253/Orbling
In one of the Discworld books, Terry Pratchett alludes to the origin of this word as being midwifery (I think it's Nanny Ogg who has the relevant line).
I imagine he just made this up though...
english.stackexchange.com/users/4877/John Bartholomew
The earliest instance of the idiom I found is from Central Valley project of California: Hearings .
United States.
Congress.
House.
Committee on Flood ControlFebruary 7-9, 1935 : page 52
It's my guess that the idiom is derived from the fixed expression push and shove , which Wikipedia calls Siamese twins or binomials.
The order of the words are never reversed and they are usually conjoined by the words and or or .
The words constituting a Siamese twins phrase may be synonyms , antonyms, include alliterations or similar-sounding words that often rhyme.
The combination: push and shove is firmly rooted in the 19th century (earlier instances I did not find in Google Books) and clearly expresses a frustrated type of struggle, where people or animals have to fight each other in order to reach their objective.
As seen in the following excerpts: Young Men's Christian Association , 1903
The Nursery by Fanny P. Searverns 1867
The Donkey and The Pigs
The London Review and Weekly Journal of Politics, Literature, Art... 1860 For the rest of us
, we push and shove ourselves into the best places, after the manner of Englishmen, that is, to our mutual discomfort, and without the least necessity ; and then we look round, and compose ourselves, to the due enjoyment of the imposing spectacle.
Missionary Chronicle Presbyterian Church in the U.S.A. Board of Foreign Missions, ‎Presbyterian Church in the U.S.A .
1844
Some go about begging and push and shove one another, [each greedy to get first].
Others go about begging unthreshed rice of the donor.
They strive for food, transgressing the rules of propriety.
They do not properly demean themselves.
From push and shove to "when push comes to shove" the path seems to me fairly straightforward.
After all what is a shove if not a more decisive and aggressive type of push?
A shove represents a surge of energy, the last resort, the final action when no alternative option is available.
english.stackexchange.com/users/44619/Mari-Lou A
I suspect it might have its origins in the 16th and early 17th century English, during the English Civil War.
The phrase that comes to mimd is a description of what happens when opposing pike blocks engaged in melee.
It was described as push of pike and musket butt.
That phrase would have percolated through the population easily since the civilian population was intimately associated with the armies.
It could easily morph into push comes to shove as that rolls off the tongue so easily and aptly describes the soldiesr in the pike blocks doing exactly that.
english.stackexchange.com/users/20365/Jones0430
"When push comes to shove" means "as a last resort" or "if absolutely necessary". Does anyone know why the phrase came to be used in this way?
What is the origin of the phrase "when push comes to shove"?
english.stackexchange.com
<etymology><expressions>
english.stackexchange.com/questions/8376
english.stackexchange.com/users/305/Brian Hooper
There is no clear agreement as to the exact origins of the phrase "when push comes to shove", although it's possible that it's meaning is essentially "when actually tested". There is a William Safire column from 1981 in the New York Times Magazine that proposes its possible origins, and it may possibly be related to a rugby scrum. It could have a rugby-related origin, but it has been seen in a 1947 book by Jacques Romain. Answers.com provides rugby-related references. One interpretation is that it means "if" v "when" with "when" being stronger.Another interpretation is that it means "when it is tested". It has developed to mean "to escalate" which is used in a business environment. It is also interpreted as starting something small, like a small fight that escalates into something bigger, the least desirable outcome of an argument. It may also have originated in the English Civil War in relation to opposing pipe blocks.
There is no clear agreement as to the exact origins of the phrase "when push comes to shove", although it's possible that it's meaning is essentially "when actually tested". There is a William Safire column from 1981 in the New York Times Magazine that proposes its possible origins, and it may possibly be related to a rugby scrum. The origin may have come from rugby and the scrum or it may have come from a midwifery term.
Terry Pratchett alluded to the origin of this expression as being from midwifery. However, others claim that it comes from the expression "push and shove", or from 16th and early 17th century English, during the English Civil War. There is no clear answer to this question, but possible origins could be midwifery, the English Civil War or the fixed expression "push and shove".
The words constituting a Siamese twins phrase may be synonyms , antonyms, include alliterations or similar-sounding words that often rhyme. The order of the words are never reversed and they are usually conjoined by the words and or or . The combination: push and shove is firmly rooted in the 19th century (earlier instances I did not find in Google Books) and clearly expresses a frustrated type of struggle, where people or animals have to fight each other in order to reach their objective. It's my guess that the idiom is derived from the fixed expression push and shove , which Wikipedia calls Siamese twins or binomials.
The words constituting a Siamese twins phrase may be synonyms , antonyms, include alliterations or similar-sounding words that often rhyme. The order of the words are never reversed and they are usually conjoined by the words and or or . The combination: push and shove is firmly rooted in the 19th century (earlier instances I did not find in Google Books) and clearly expresses a frustrated type of struggle, where people or animals have to fight each other in order to reach their objective. It's my guess that the idiom is derived from the fixed expression push and shove , which Wikipedia calls Siamese twins or binomials.
It may be a rugby scrum origin theory. I found a  snippet  of a 1981 William Safire column in  New York Times Magazine  article that indicates this guess was put forth by an AJ Gracia of Southbury, Connecticut. S8: Safire wrote  another column  on the phrase in 1997 which drops the mention of rugby altogether. I found the phrase used over a decade earlier ( 1947 ) in the English translation of Haitian Jacques Romain's  Masters of the Dew  done by Langston Hughes and Mercer Cook. There are other rugby references: Answers.com  also cites the rugby reference.   It also notes the other meaning of the phrase as in "They supposedly support equality, but when push comes to shove they always seem to promote a man instead of a woman".   I think the difference is "if" vs. "when".    I see think the "when" meaning is more prevalent.   It means "when actually tested".   Push is just a push, and things have escalated to a shove now.    It now means business.   Escalate to get the thing accomplished. Pushing and shoving is a way of referring to fighting, particular little man-to-man arguments.   They start with a push and a shove, so when "push comes to shove", it means a fight will break out.   Fighting is the last resort, or at least the least desired outcome of an argument. S5: It's my guess that the idiom is derived from the  fixed expression  push and shove , which Wikipedia calls  Siamese twins  or binomials. S6: The order of the words are never reversed and they are usually conjoined by the words  and  or  or .       S7: The words constituting a Siamese twins phrase may be  synonyms , antonyms, include alliterations or similar-sounding words that often rhyme.    S8: The combination:  push and shove  is firmly rooted in the 19th century (earlier instances I did not find in Google Books) and  clearly expresses a frustrated type of struggle, where people or animals have to fight each other in order to reach their objective.   S22: A  shove  represents a surge of energy, the last resort, the final action when no alternative option is available.    It may have origin in the English Civil War.
The origin may be from rugby, describing a scrum. The origin may be from midwifery. 
There is no clear answer to this question, but possible origins could be midwifery, the English Civil War or the fixed expression "push and shove".