President Obama and Republican Mitt Romney both spent Tuesday in Ohio, a crucial state that has suddenly become much more competitive now that Romney has caught post-debate momentum.

Obama had been leading Romney by as much as 10 percentage points in Ohio prior to their Oct. 3 debate. But Romney's dominating debate performance has nearly erased that lead. A CNN/ORC International poll released Tuesday showed Obama with 51 percent of the vote among likely Ohio voters and Romney with 47 percent, a statistical tie given that the difference is within the poll's margin of error.

The CNN poll and other post-debate surveys are in line with Romney's internal polling, which shows a suddenly very competitive race in Ohio. Romney's aides now insist he can win Ohio, a state won by every Republican who went on to win the White House, but one Obama won four years earlier.

Ohio could potentially determine the outcome of the presidential election as it did in 2004, when President George Bush beat Democratic nominee John Kerry by just 110,000 votes to clinch a second term.

With the election a month away, both candidates are pouring energy and resources into winning Ohio, including a flurry of television and Web-based advertising and regular campaign stops that have attracted thousands.

In addition to visiting Ohio on Tuesday, Romney will make two joint appearances there Friday with his vice presidential running mate, Paul Ryan, who will be coming off his Thursday night debate with Vice President Biden.

Obama this time around switched strategies and is no longer trying to win over the rural voters who provided part of his 4-percentage-point margin over Republican John McCain in 2008. Obama now is focusing on urban and college-age voters.

The president appeared at a rally Tuesday at Ohio State University in Columbus. Last week, he visited Bowling Green State University and Kent State University.

While Obama's support for an auto-industry bailout has bolstered his standing among the blue-collar voters of Ohio, his environmental policies have cost him the support he had in coal-rich southeast Ohio, where he did well in 2008.

"Obama has been branded anti-coal by the coal industry," said Thomas Sutton, a pollster and political science professor at Baldwin Wallace University.

The Obama campaign is now looking to the state's cities, and particularly to African-American voters in those areas, to counter those losses.

"It's a shift for the Obama folks," Sutton said. "Four years ago, they did more broad-based efforts that reached into rural areas."

Even as the polls show Romney closing the gap in the Buckeye State, Obama may still hold an advantage in the state because of his extensive get-out-the-vote operation, particularly on college campuses, said Ohio State University professor Erik Nisbet.

"Romney has not made one visit to Ohio State," Nisbet noted.

Romney's growing support in Ohio mirrors the momentum he's gained nationwide. A heavily anticipated survey of likely voters by Gallup released Tuesday shows Romney leading Obama 49 percent to 47 percent nationally, a spread within the poll's margin of error but evidence nonetheless that support for Romney has been growing since he bested Obama in their first debate.