ABC is out with an extremely Republican-friendly sequestration poll noting that most voters say they back the idea of a 5-percent cut in federal spending, but cutting the military is unpopular. I have no doubt that's an accurate reflection of public opinion, but it's also an extremely misleading way to frame it.
The correct context for this is a Pew poll that asked about many categories of spending and found majority support for cuts in exactly zero categories. Decrease spending is a plurality position on foreign aid and nothing else. For the State Department and aid to the unemployed, keeping spending constant is the plurality position, but spending hawks outnumber increasers. On every other category, more voters prefer an increase in spending to a decrease. In some categories (military, 32-24; aid to the domestic poor 27-24) the margin is relatively narrow, whereas in others (Social Security, 41-10; veterans, 53-6) the margin is enormous.
Long story short, public opinion on budgetary matters is poorly structured and there isn't a clear and internally consistent policy agenda that you can read from the polls. So if you constructed any ABC-style poll in which you first ask about spending cuts and then ask about one particular program, you'd get the ABC result that people want big spending cuts but also want to exempt Program X from the cuts. But that's just a kind of cheap trick. Relative to other programs, cuts to military spending are among the least unpopular cuts around.