In the last 13 presidential terms most Democratic presidents (4 out of 6) reduced the size of government while most Republican presidents (5 out of 7) increased its size.
Using government data one can make a "scorecard" for each 4-year administration for Federal employment (excluding military) for the past 13 4-year presidential administrations. The results: Democrats--4 administrations decreased federal employment while 2 increased it; Republicans--2 administrations decreased federal employment but 5 increased it.
A terrific government website lists total Federal government employees by year.
opm.gov With this one can easily check to see whether an administration has increased or decreased federal employment (conveniently broken down by executive branch, military, or judicial/legislative).
Using the data from that website here are the changes in the size of government (excluding military) for the last 13 4-year administrations:
D Johnson -15,000 (note approximation using data only to 1962)
D Johnson +550,000
R Nixon -197,000
R Ford +10,000
D Carter -12,000
R Reagan +33,000
R Reagan +200,000 (isn't this interesting!)
R Bush -37,000
D Clinton -231,000
D Clinton -147,000
R Bush +11,000
R Bush +42,000
D Obama +5,000 (note, this is the first term only)
Surprisingly, a parallel assessment of the military employment figures shows that by far the greatest reductions in military personnel occurred in Republican administrations (5 out of 7) while Democratic administrations reduced the military, but by far smaller numbers, in 4 out of 6 terms.
This simple assessment appears to contradict the often-heard conventional wisdom that Republicans favor smaller government.