I would argue that the US has been in a conservative period at least since the election of Ronald Reagan in 1980 and probably since the election of Richard Nixon in 1968. This has come about as a backlash against the economic policies of Lyndon Johnson and the social upheaval of the 1960s.
Richard Nixon argued that he represented the "silent majority" of people who did not go out and protest the Vietnam War or become hippies. He represented a backlash against those people and their values. I would argue that the current conservative cycle in American politics dates to that backlash. The backlash has also been made more intense by the increasing size of the federal government. The government exploded under Johnson and has not really shrunk to any great degree. This has helped bring us to our current situation with a tremendous government deficit and debt and a very angry Tea Party movement pushing against the idea of big government.