I continue to believe that the Obama campaign is angling to fight Mitt Romney to a draw on the economy. As I’ve noted before, Obama advisers would obviously like a win, but they many have to settle for a draw. Then the campaign might be winnable on other fronts: tax fairness, entitlements, vision for the future, personal attributes.

Today’s New York Times/CBS/Quinnipiac poll of three swing states sheds a bit more light on this. They suggest an interesting dynamic has taken hold. Swing voters continue to say Obama is more in touch with their problems than Romney; and they mostly see his business background negatively. But Romney is tied with Obama — or doing better — on the generic question of who can fix the economy.

Romney’s numbers are upside down on whether he cares about people’s problems in Wisconsin (41-51) and Virginia (44-48). They are roughly even in Colorado (47-46). By contrast, majorities in all three states say Obama cares about their needs and problems.

Meanwhile, pluralities say Romney’s business background was too focused on profits, rather than the right experience to get the economy going, in Virginia (47-43) and Wisconsin (48-43). (In Colorado, Romney is doing better, with 48 percent saying Bain is the right experience.)

And yet, on who would do a better job on the economy, Obama and Romney are roughly tied in Wisconsin (47-46) and Virginia (45-47), with Romney having a bigger lead in Colorado (51-41).

This is similar to other swing states: A recent NYT/CBS poll found a majority of voters in Ohio and Pennsylvania, and a plurality in Florida, don’t think Romney understands their needs. But in all three the two were tied on the economy.

It seems fair to assume swing state voters are forming an image of Romney as someone with a corporate executive’s worldview that is alien to them, and as someone whose previous life was spent amassing wealth for himself, rather than creating jobs. At the same time, those voters are willing to grant Romney the general presumption of competence on the economy, perhaps partly as an alternative to their disillusionment with Obama and the status quo.

With Obama continuing to dominate on the question of which candidate cares about ordinary people’s needs and problems, is it too early to say that the “didn't build that” attacks, which are designed to paint Obama as disdainful of their hard work, are not working?

After all, these numbers are what the sparring over “didn’t build that” and Bain alike are all about. If Obama can neutralize Romney on the economy — if voters conclude that Romney doesn’t necessarily have the answer to their problems — they may make the call on which candidate they think will really fight for them and can be trusted to protect their interests in a host of areas — taxes, entitlements, health care. That’s why Romney is hitting the “didn’t build that” speech so ferociously — to close the empathy gap by pulling Obama down in this area. The state of the economy may still tilt voters against Obama on election day, but for now, Romney is struggling to close that gap.