Entry in progress—B.P.
 
A modern jocular variant is “Throw the Rascals In!”
   
Wikipedia: List of U.S. presidential campaign slogans
Turn the Rascals Out - 1872 anti-Grant slogan against the Era of Good Stealings
 
28 July 1872, New York (NY) World, pg. 1, col. 5:
Witness also testified to Judge Barnard saying he had driven one set of d—d rascals out of the State, and he would drive another.
 
Google Books
American Sayings:
Famous Phrases, Slogans and Aphorisms
By Henry F. Woods
1945, 1949; 2008 reprint
Pg. 46:
“Turn the rascals out.”
Charles Anderson Dana (1819-1897)
HORACE GREELEY, famous editor of the New York Tribune, was the candidate of the Liberal Republican Party for President in 1872, running against General U. S. Grant, the regular Republican candidate for re-election. Greeley’s campaign was waged on the issue of the necessity for reform in the national administration, which under Grant had been marked by grave scandals, and the cry “urn the rascals out” was adopted as a party slogan.
 
The phrase was originated by Charles A. Dana, editor of the New York Sun, who had broken with Grant in 1869 and thereafter attacked his administration with exceptional bitterness. Although Dana’s antagonism to Gran continued unabated, his support of Greeley’s candidacy was not remarkable for any great fervor or force, and Greeley was defeated by Grant.