Mr. Obama’s goal is to keep Mr. Romney from running up huge margins among white working-class voters — defined as those without college degrees and with household incomes of $30,000 to $100,000 — who could give him the edge.

New results from surveys over the past week in Colorado, Virginia and Wisconsin, combined with surveys last week in Florida, Ohio and Pennsylvania, show that Mr. Romney so far appears to be holding his own with that group, but running no stronger than Senator John McCain did four years ago.

Similarly, Mr. Romney is trying to peel off as many female voters as possible from Mr. Obama’s electoral coalition, hoping to offset the president’s advantages among single and nonwhite women by appealing to married and white women with a message about economic security and pocketbook issues.

But while the poll suggests that Mr. Romney is making inroads among women in Colorado, where he is also showing strength against Mr. Obama by several other measures, support for Mr. Obama among women has otherwise held up in the battleground states. As a result, Mr. Obama has so far been able to stave off bigger losses in the most hotly contested states, in particular among independents, who are divided in Colorado and Wisconsin and supporting Mr. Romney in Virginia, and white men, who are supporting Mr. Romney by double digits over the president in all three states.

Far more than national polls, which can track the mood of the electorate only as a whole, the results in the state-by-state polls provide a detailed snapshot of the race where it matters most, in geography and demography. They also help explain why both the Obama and Romney campaigns are focusing so much of their time and money on messages intended to resonate with such specific groups in such specific places.