I define a stretched presidency as lasting a minimum of eight years and including a presidency of the person elected plus potentially the consecutive presidency of her or his (it has always been his thus far) vice president. The original president wins re-election and/or the vice president of the president wins a consecutive term when the president leaves office (due to term limit, death, or conviction for impeachment or potentially due to choice).
Since Franklin Delano Roosevelt became president in 1933, 84 years ago, only once has a presidency not stretched: with the electoral loss by one-term president Jimmy Carter to Ronald Reagan in 1980.
Once we account for the stretchedness of presidencies—seeing vice presidents replacing and becoming presidents as part of an uninterrupted unit with the presidency in which they originally served as vice president—we see that since 1933 in the United States parties have alternated being in power at the presidential level in stretches, as we’re defining it, again with the exception of President Carter. Equally importantly, parties have not held power for longer than those stretches: it has been nearly 90 years since someone who was not vice president has taken presidential office following someone of the same party without the other party winning office first. (The last time such a transition happened was when President Hoover was elected in 1928 and replaced President Coolidge, another Republican.)
Stretched Presidencies Since 1933 (Plus the One Unstretched Presidency)
Democratic/President Roosevelt-President Truman: 1933-1953 (20 years)
Republican/President Eisenhower: 1953-1961 (8 years)
Democratic/President Kennedy-President Johnson: 1961-1969 (8 years)
Republican/President Nixon-President Ford: 1969-1977 (8 years)
Democratic/President Carter: 1977-1981 (4 years — unstretched)
Republican/President Reagan-President Bush (H.W.): 1981-1993 (12 years)
Democratic/President Clinton: 1993-2001 (8 years)
Republican/President Bush (W.): 2001-2009 (8 years)
Democratic/President Obama: 2009-2017 (8 years)
Finally, setting aside the notion of stretched presidencies and extending our look simply to parties in power at the presidential level and their tendency to alternate in blocks of time of eight or more years: the last time other than the Carter presidency that a party didn’t have at least eight consecutive years in office was during the presidency of Grover Cleveland, a one-term Democratic president from 1893 to 1897. Subsequent to that, leading into the above list of stretched presidencies:
Republican/President McKinley-President Roosevelt-President Taft: 1897-1913 (16 years)
Democratic/President Wilson: 1913-1921 (8 years)
Republican/President Harding-President Coolidge-President Hoover: 1921-1933 (12 years)
In other words, with the sole exception of the four-year, post-Watergate, post-pardon term of President Carter, Democrats and Republicans each have held control of the White House for stretches of eight years or more unceasingly for 120 years.