COLUMBUS, Ohio — As President Obama and Mitt Romney enter the closing week of the presidential race, where the 18 electoral votes of Ohio are seen by both sides as critical to victory, Mr. Obama’s ability to prevent erosion among working-class voters may be his best path to re-election.

In Ohio, according to the latest poll of likely voters by Quinnipiac University/New York Times/CBS News, Mr. Obama runs nearly even with Mr. Romney among white voters who do not have college degrees.

That helps explain why he appears slightly better positioned there in the closing week of the campaign than in Florida and Virginia, where the polls found that Mr. Romney holds an advantage of about 30 percentage points among those voters.

The presidential contest has become an intense state-by-state fight, with the climate in Ohio shaped by months of efforts by the Obama campaign to portray Mr. Romney as a job killer who opposed the president’s decision to bail out the auto industry.