Seeking to create more options and influence voters in neighboring states, Romney has made modest television advertising investments in Minnesota and Maine, competing in states that haven’t supported a Republican in at least two decades.

Ohio and Wisconsin, where Democrats have an edge, have emerged as linchpins to his strategy.

Democratic strategists say that Romney’s opposition to the auto bailout that resurrected the American auto industry continues to hurt him across the industrial Midwest. Obama seized on Romney’s position during last week’s third and final debate, a moment Democrats say helped reverse the Republican candidate’s momentum among working class white voters, an important constituency in blue-collar Ohio.

‘‘To his credit, Romney got himself back into the race. But it’s not enough,’’ said Tad Devine, a Democratic strategist and senior adviser to 2000 and 2004 presidential nominees Al Gore and John Kerry.

Still, Romney was greeted by large enthusiastic crowds in the thousands in Ohio, Iowa and Florida in recent days, a sign Republican pollsters and strategists attributed to higher intensity of support from his campaign’s base.

Romney aides suggest that swing-state polls overestimate Obama’s support. Obama aides dismiss polls showing Obama losing support among women.

‘‘It’s going to be a tight race right to the end,’’ said Romney senior strategist Eric Fehrnstrom. ‘‘But we’re riding a wave and it hasn’t hit the beach yet.’’

Both sides agree this race will be won at the margins.

That explains why Obama’s campaign has been working hard to undercut Romney’s support among women by citing links between Romney and an Indiana Senate candidate, Richard Mourdock, who drew fire for saying that pregnancies resulting from rape are ‘‘something God intended.’’ Romney aides said he disagreed with the comment but Romney himself refused to condemn the remark or call on Mourdock to remove TV ads the GOP presidential nominee had filmed for him.

The renewed attention on abortion came just as polls showed Romney having narrowed Obama’s advantage with women. Now Democratic pollsters say they see evidence that Romney may be losing those gains among women, especially in Virginia and Colorado.

Not that he’s ceding ground.

‘‘These are tough times for middle-income Americans,’’ Romney said Friday night in North Canton, Ohio. ‘‘How many single moms these days are scrimping and saving so they can put a good meal on the table at the end of the day for their kids?’’

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