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For all of the Democratic attacks painting Mitt Romney as an out-of-touch elitist who will help the rich at the expense of the middle class, he is maintaining the traditional — and sizable — Republican advantage among a politically vital constituency, white working-class voters in the states most likely to decide the presidential election.


And despite Republican efforts to use the weak economy to drive a wedge between President Obama and women on Election Day, the president is holding on to their crucial support in most battleground states.


Those findings, contained in the latest batch of Quinnipiac University/New York Times/CBS News swing state polls, highlight the stubborn divisions of this year’s presidential race among two of the most important voting groups in the most hotly contested states.


But they also help explain the intense efforts of the two campaigns to alter the balance in both groups, which together will go a long way toward determining the outcome.


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.


The latest polls underscore just how tight the race continues to be, with the candidates running closely in Virginia and Colorado and Mr. Obama leading in Wisconsin, though not by his double-digit margin of victory in 2008. Mr. Obama won all three states in 2008.


Mr. Obama is struggling because of the economy and facing new challenges in Colorado, where his support among white men has fallen considerably from where it was in exit polls there in 2008.


But Mr. Romney is also struggling to connect with middle-class voters. And about half of voters in each of the three states said presidential candidates should release several years of tax returns. (Mr. Romney has so far declined to release more than two years of returns amid calls by Democrats and even Republicans for more.)


Combined with the surveys last week in Florida, Ohio and Pennsylvania, the new state polls paint a portrait of an electorate that has largely made up its mind but sees both candidates as having vulnerabilities — giving each side opportunities to exploit.


In all three states, more voters said that Mr. Obama’s policies would hurt their personal finances if he were elected to a second term than said they would help.