A politician who will go to any lengths to win public office, regardless of party affiliation or platform.
One of the earliest references comes from the Columbus Dispatch in October 28, 1895 which defined the term as “a fellow who wants office, regardless of party, platform, or principles, and who… gets there by sheer force of monumental talknophical asumnancy.”
According to Vintage Vocabulary, President Harry Truman revived its use in 1952. Talking about politicians who like to make a show of public prayer, he said, “I wish some of these snollygosters would read the New Testament and perform accordingly.”
Time notes Truman’s tone “left no doubt that a snollygoster was a low creature indeed, but few, if any, of his hearers knew what snollygoster meant.”
A related term is carpetbagger.