I personally just think it's part of the well-documented phenomenon of people becoming more conservative during lean economic times. That, and decades of conservative messaging. A well-designed healthcare system could turn this all around.
The new NBC News/Wall Street Journal had a similar question in its poll, but found different results (pdf). Respondents were asked whether government "should do more to solve problems and help meet the needs of people" or government "is doing too many things better left to businesses and individuals."
A narrow plurality preferred the latter, 49% to 45%, but the 49% is the highest anti-government-activism rating in several years. Note, however, that there was only a four-point gap between the two -- in the Gallup poll, it was a 19-point gap between those who think government is doing too much, and those who want it do more.
Of course, I generally tend to think the government ought to be doing quite a bit more--healthcare, of course, plus climate change, stricter financial regulation/oversight, labor and vacation reforms and some serious education reform that includes making college more affordable--but there are certainly areas where it ought to be doing quite a bit less: I'd favor halving defense spending and decriminalizing soft drugs, to start with, along with a major reform of the federal prison system and some sort of means-testing of entitlements (and ending Social Security survivor benefits). While I would like to see the government provide more stability and opportunity for people, I am not a huge fan of the more egregious nanny-statery you see out there. Banning smoking in public places seems fine to me--I see it as less about smokers' rights and more about nonsmokers' rights to breathe, which seems more fundamental to me--but some of the more recent laws on the topic seem excessive.