First, it's worth noting that Romney and Republicans did take Obama's remarks out of context in a way which changed their meaning. The most common quote I've seen from the conservatives is, "If you've got a business, you didn't build that." Obviously this sounds like Obama is telling people who have their own business that they don't deserve credit for it--the government did the work for them. That would be offensive and inaccurate. Building a business requires both tremendous effort and a high tolerance for risk. Those who are able to do so deserve the overwhelming majority of the credit, even if luck and government play some role.
But that's not what Obama said. Here's the whole quote:
If you were successful, somebody along the line gave you some help. There was a great teacher somewhere in your life. Somebody helped to create this unbelievable American system that we have that allowed you to thrive. Somebody invested in roads and bridges. If you’ve got a business -- you didn’t build that. Somebody else made that happen.
Even if you think Obama really believes that government built everyone's businesses, it's a stretch to think he'd say it in public. I think a reasonable reading of the full quote suggests that Obama is simply stating that if you have a business, you didn't build the "American system" that enabled your business to succeed. That's largely true. Business occurs within an environment of things like government-provided infrastructure, the education system, and a set of laws which sometimes are conducive to commerce (sometimes). Fair enough. Romney was disingenuous to claim that Obama thinks Henry Ford didn't build Ford, and all the rest.
But that doesn't let Obama off the hook. He made this statement as part of an argument for higher taxes on the wealthy. His apologists have cited things like roads and schools as examples of things businesses didn't build that justify higher taxes on certain people. But there are two problems with that argument. First, roads and schools and other government-provided amenities aren't the result of some benevolent government entity, providing for its people as a mother feeds a child. Those things are paid for by, well, people, including (and especially) rich people. And I don't hear many people on the right complaining about having to pay for roads and bridges (well, except bridges to nowhere).
Second, the higher taxes Obama wants are not even meant to pay for roads and schools. Current taxes are more than sufficient to finance those items. The taxes Obama wants are meant to pay for our massive warfare/welfare state. Here's a chart from the Center on Budget and Policy Priorities (click for larger image):
Observe that transportation infrastructure and education comprise 5 percent of the federal budget (indeed, state and local government are more relevant for those categories). The overwhelming majority of the federal budget--81 percent!--goes to defense and entitlements, the warfare/welfare state. If you're looking for the drivers of government's insatiable thirst for tax revenue, there they are. Estimate the tax burden needed to actually pay for our whole budget, then divide that number by 20. Now you have roughly enough revenue to pay for the roads and bridges and schools. You could double spending on those items and still be able to lower taxes if it weren't for the warfare/welfare state.
So, setting aside businesses designed to feed at the government trough, it's not clear that Obama's point about a government-created atmosphere helping businesses actually justifies higher taxes on high earners. In short, Obama is using the benefits of infrastructure to justify taxes to finance the ever-expanding warfare/welfare state. That's disingenuous.
Now if only we had candidates with plans to rein in the warfare/welfare state...