The following table lists how many of the major agencies or departments had their budgets cut in a given Presidential term:
President and Term, Number of Budget Cuts [see the last link in this post for further explanation of the data. I’ve done minor editing and added the boldface]
Johnson, 4 out 15
Nixon, 3 out 15
Carter, 5 out 15
Reagan 1, 8 out 15
Reagan 2, 10 out 15
Bush, George H., 2 out 15
Clinton 1, 9 out 15
Clinton 2, 0 out 15
Bush, George W., 0 out 15
Obviously Reagan II made real efforts in this direction. George W. comes in tied for last with Clinton II. This is a highly imperfect proxy, but when you are 0 for 15 it is hard to blame measurement error alone.
Here is one unnoticed achievement of Ronald Reagan:
President Reagan is the only president to have cut the budget of the Department of Housing and Urban Development in one of his terms (a total of 40.1 percent during his second term).