Among D.C. politicians, all Republicans and most Democrats favor cuts in spending on Social Security, Medicare, and Medicaid (i.e. "entitlements"). Some big policy disagreements exist about how you want to do that, but the main disagreement is that Democrats want such cuts to be part of a "balanced" deficit reduction strategy while Republicans reject tax hikes.
Defense spending reductions, meanwhile, are much less popular. There's a nontrivial bloc of congressional Democrats who favors major reductions, but that's not a stance embraced by party leadership or recent presidential candidates. But as a recent Economist/YouGov poll confirms—key result replicated above—public opinion is pretty different. An overwhelming 71 percent of the population says it favors spending cuts to reduce the budget deficit, but cuts to Social Security, Medicare, and Medicaid are all unpopular. Defense cuts, by contrast, poll pretty well. The modern-day version of the guns or butter choice is guns or grandma's hospital bills, and the public clearly prefers grandma's hospital bills.
And something that's interesting is that back during the debt ceiling talks, when we finally got down to the wire and the gun was to John Boehner's head he decided he would rather risk large defense cuts via the sequester process than agree to higher taxes.
Which isn't to say Republican elites have embraced defense cuts. The GOP swiftly turned around and started slamming Democrats for cutting defense. Meanwhile, on the campaign trail Obama insisted the sequester cuts wouldn't happen and would instead be replaced by higher taxes on the rich. So even though when the heat was on both sides agreed to cut defense, neither party is yet willing to "own" this position. But it polls better than alternative cuts. I recently read David Karol's Party Position Change in American Politics which reveals that the politics of the defense budget is one of the most frequently flip-flopped non-procedural issues in modern politics. It's one where party leaders seem relatively unconstrained by constituency group commitments or ideology, and fairly free to engage in freelance gambits of various kinds. So given the gap between current polling and current elite positioning, it's a place where we might expect to see some surprisingly rapid changes.