“Off the reservation” means, in political terms, a party member who does not adhere to party principles (the “reservation”). The term “off the reservation” has been in use since at least the 1890s.
   
 
(Oxford English Dictionary)
reservation, n.
(...)
9. orig. U.S. Originally: an area of land set apart or reserved by the government for occupation by American Indians, esp. by those of a particular tribe or nation. Later also more generally: any area of land reserved for a special purpose, e.g. for military use, for the protection of wildlife, etc. Cf. RESERVE n. 5b.
Freq. with preceding modifying word. Indian, military reservation, etc.: see the first element.
1789 Deb. Congress U.S. 25 May (1834) 41 The reservation,..of six miles square round the fort at Oswego, is within the territory of the State of New York.
1792 Let. 8 Aug. in Mass. Hist. Soc. Coll. (1806) 1st Ser. I. 287 The whole Six Nations live on grounds, called the State Reservations, and are intermediate spaces settled on both sides by white people.
1803 in U.S. Statutes at Large (1850) II. 225 So much of that tract, commonly called the ‘Virginia military reservation’, as will amount to one thirty-sixth part of the whole tract.
1830 J. GALT Lawrie Todd II. IV. xii. 100 Without touching the reservation round Judiville.
1859 J. S. HELMCKEN Let. 25 Jan. in Archives Brit. Columbia. Memoir No. IV (1918) 45 Has the Government of this Island [sc. Vancouver Island] the power to remove the Indians (by purchase) from that piece of land inside Victoria Harbour known as the Indian Reservation?
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U.S. to go off the reservation and variants: to deviate from what is expected or customary; to behave unexpectedly or independently. Hence also on (also on to) the reservation.
With allusion to sense 9.
1898 F. REMINGTON in Harper’s Mag. Nov. 962/2 The fires of hatred burned within me. I was nearly overcome by a desire to ‘go off the reservation’. I wanted to damn some official, or all officialism.
1926 Washington Post 6 Jan. 17/7 Art Nehf..is a lefthander but a trusty. Mr. Nehf never goes off the reservation.
1937 S. HIGH Roosevelt—& Then? viii. 187 It was no simple matter to keep Lewis on the reservation… He all but packed his bags for a trip into political seclusion.
1960 H. S. TRUMAN Let. 31 Jan. in Strictly Personal & Confidential (1982) 137 I’ll never forget 1948 when these so called ‘liberals’..went off the reservation and gave New York to Dewey.
 
8 February 1899, Kansas City (MO) Star, “The Democrats at Sea,” pg. 2:
Holding to their patronage with one hand and defending themselves from dissatisfied constituents on the other confronted by the certain knowledge that the big well-organized Republican minority is waiting for a chance to join hands with any faction that decides to go off the reservation, the Democratic caucus lacks that feeling of harmony that a well organized, majority needs to make its efforts at reform effectual.
 
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1 July 1910, The Reform Bulletin (Albany, NY), pg. 3:
Notwithstanding the vote on the Cobb bill yesterday, direct primary reform now is a Republican party principle, and those who oppose it are, as they have said of others, “off the reservation.” (...)—Troy Record.
       
Google Books
La Follette’s winning of Wisconsin (1894-1904)
By Albert O Barton
Madison, WI
1922
Pg. 129:
We told him that we were republicans, but believed in certain progressive principles, and succeeded in sending the delegation back somewhat reassured, but they warned us against getting off the reservation.
 
Google Books
From Harrison to Harding, a personal narrative, covering a third of a century, 1888-1921
By Arthur Wallace Dunn
New York, NY: G.P. Putnam’s Sons
1922
Pg. 106:
It antedated the death of Senator Allison, when Dolliver showed a disposition to “get off the reservation.”
 
Google Books
This man La Guardia
By Lowell M Limpus and Burr Watkins Leyson
New York, NY: E. P. Dutton
1938
Pg. 175:
CHAPTER XII
OFF THE RESERVATION
 
POLITICO.com
Progressives: Go off the reservation
By ROBERT L. BOROSAGE
6/3/10 11:48 PM EDT
(...)
History demonstrates that progressive movements best effect change in Democratic administrations when they organize independently.
 
We must be “off the reservation”—like labor was under President Franklin D. Roosevelt, and the Civil Rights Movement was under President Lyndon B. Johnson.
 
Johnson wanted Martin Luther King Jr. to shut down the demonstrations, asserting that they would make reform impossible. With an independent movement, King could not have done that even had he wanted to. Instead, he went to Selma, Ala., and the resulting confrontation led directly to passage of the Voting Rights Act.