In the first presidential debate, Mitt Romney said he would eliminate federal funding for PBS. President Obama and other Democrats have frequently reminded people of that, which suggests they think that it's an unpopular position. A CNN/Opinion Research Corporation survey in 2011 gave people a list of ten programs, and asked if federal funding should be increased, kept the same, decreased a little, decreased a lot, or eliminated entirely. If you give the options scores of 1 to 5, with 1 representing a spending increase and 5 representing elimination, the averages are:
Social Security 1.78
Housing assistance for poor 2.06
Food for poor 2.08
Military spending 2.21
Gov't pensions 2.68
Public broadcasting 2.74
Foreign aid 2.91
So spending for public broadcasting is second from the bottom in terms of public priorities, finishing ahead of only "aid to foreign countries for international development and humanitarian assistance" (the survey included descriptions of most of the programs--I just give shortened labels). So Mitt Romney was right to go after PBS, at least in a political sense. The relative lack of support for public broadcasting probably doesn't
represent anti-intellectualism, since education spending gets the most
support. My guess is that people see public broadcasting as less essential, or something that could be replaced by private contributions.
On the other hand, people aren't in favor of big cuts in any program--the mean is in favor of increasing spending for education, Medicaid, and Social Security and at keeping spending the same for Medicaid (which the survey describes as "the federal health program for the poor"). Even for foreign aid, the mean was in between kept the same and decreased a little.