Entry in progress—B.P.
 
Wikipedia: Mexican standoff
Mexican standoff is a strategic deadlock or impasse, in which no party can act in a way that ensures victory.
 
Origins
The phrase came into usage during the late 19th century. Originally a reference to perceived Mexican political indecision, it has come to refer to any impasse, regardless of the participants or the presence of arms.
 
In popular culture
In popular culture, the Mexican standoff is often portrayed as three or more opponents with weapons aimed at each other, such that each opponent feels equally threatened and does not believe he can strike first without endangering his own life; not only does any initial shot decisively destroy the unstable equilibrium of multiple deterrence, shooting any one person takes one’s aim away from the other opponent. Note that two people with weapons pointed at each other is a simple standoff.
 
The Mexican standoff has been used in many film genres such as spaghetti westerns or action films. Famous cinematic examples can be seen in the 1960s classics The Good, The Bad And The Ugly or Once Upon a Time in the West, as well modern movies like City on Fire, Die Hard, Hard Boiled, Pulp Fiction or Reservoir Dogs and at the end of Enemy of the State.
 
Historical Dictionary of American Slang
Meixcan standoff n.
1. a deadlock resulting from the opposition of equally powerful adversaries; an impasse from which neither party dares to withdraw; stalemate.—now often considered offensive. Noww colloq.
1891 in DARE: “Monk” Cline, who got a Mexican stand-off from Dave Rowe, has signed with louisville.
1929 J.M. Saunders Single Lady 241: it would be about a Mexican stand-off.
1935 Pollock Und. Speaks: Mexican Stand-off, no chance to win.
(...)
2. a partial victory or defeat; an unsatisfactory but roughly even outcome.—now often considered offensive.
1904 in DARE: Boys, as fur as the coin goes, we’re out an’ inured; we jest made a “Mexican stand-off”—lost our money, but saved our loves—and mighty lucky at that.
1921 T.A. Dorgan, in Tamony

(No. 19) 7: They got a “Mexican Standoff.” That is to say, they lost their money but saved their lives.
1926 C.M. Russell Trails 48: The way they start pilin’ lead in our direction makes us hug the brush; we don’t leave it till dark….It’s a Mexican stand-off, which means gettin’ away alive.
   
(Oxford English Dictionary)
Mexican standoff n. [see STAND-OFF adj. 3] a deadlock, stalemate, impasse; a roughly equal (and freq. unsatisfactory) outcome to a conflict in which there is no clear winner or loser; (also formerly) a massacre in cold blood.
1891 N.Y. Sporting Times 19 Sept. 4/3 ‘Monk’ Cline, who got a *Mexican stand-off from Dave Rowe has signed with Louisville.
1904 in Dict. Amer. Regional Eng. (at cited word), Boys, as fur as the coin goes, we’re out an’ injured; we jest made a ‘Mexican standoff’—lost our money, but saved our lives.
1934 J. O’HARA Appointment in Samarra (1935) vii. 222 The men were the victims of the St. Valentine’s Day massacre in Chicago, when seven men were given the Mexican stand~off against the inside wall of a gang garage.
1958 ‘W. HENRY’ Seven Men at Mimbres Springs xvi. 189, I rightly and firmly believe we’ve taken some of the flap out of Mangas’s shirttails and can turn this thing into a Mexican stand-off, given any luck at all.
 
14 February 1895, Idaho Statesman, pg. 1:
Neill, in reply to Wyman, said it was a “Mexican stand-off” so far as the people were concerned. They might win their case, whether civil or criminal, but the lawyers would get all their money.
 
Henry retorted he did not know exactly what a “Mexican stand-off” was, but Neill was the best practical illustration he had ever seen.
 
Google Books
Thirty-One Years on the Plains and in the Mountains
Or, The last voice from the plains
By Capt. William F. Drannan
Chicago, IL: Rhodes & McClure Publishing Company
1903
Pg. 480:
In those days this was what we called a Mexican stand-off. I lost my time and money, but had my life left.