The basis for the phrase is that the United States, following the War of 1812, settled into a period of rule by one party, the Democratic-Republicans of Monroe (which had their roots in the Jeffersonian Republicans).
This period in history was actually misnamed, as there were a number of tensions developing in the United States. For instance, a major crisis over slavery in America was averted by the passage of the Missouri Compromise (and that solution was, of course, only temporary).
The very controversial election of 1824, which became known as "The Corrupt Bargain," brought an end to this period, and ushered in the troubled presidency of John Quincy Adams.
Related: The Monroe Doctrine


