President Obama assailed Mitt Romney for “top-down economics” in his ninth trip this year to this battleground state, brandishing a new study showing that Mr. Romney’s plans would mean additional large tax cuts for millionaires at the expense of other Americans.

Mr. Obama’s appearances in north-central Ohio, first in Mansfield and then here, came as new polls continue to show voters split over his stewardship of the economy. He will take his case to Florida on Thursday, but on Friday the release of the monthly unemployment report could do more than any presidential words to shape voters’ views.

Facing an estimated 3,000 people at a convention center here, Mr. Obama was fired up as he explained what his campaign characterizes as the fundamental differences between him and Mr. Romney over tax and spending priorities at a time of rising debt.

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