SAN FRANCISCO » With swinging polls making the White House race as unpredictable as ever, President Barack Obama and Republican challenger Mitt Romney were crossing Ohio today and making their case with new urgency in the campaign’s final weeks.

Obama maintains more paths to victory, but polling shows a tightening race after more than 67 million people watched Romney shine in their debate in Denver last week. The challenger’s math is extremely narrow, particularly without Ohio. No Republican has won the presidency without carrying the state.

Based on the presumed outcome of the 41 non-battleground states and Washington, D.C., Obama enters the final period banking on 237 electoral votes. Romney is assured of 191.

On the road to the 270 electoral votes needed to win the presidency, nine battleground states — Ohio, Florida, Iowa, Nevada, Wisconsin, New Hampshire, Virginia, North Carolina and Colorado — account for the final 110 votes.

Both Democrats and Republicans say internal campaign surveys after last week’s debate show Romney cut into the lead Obama had built in many key battleground states. But they say Obama still has an advantage in most of them.

The two candidates today were focusing on Ohio, where Obama had opened a lead before the debate. Romney also planned stops there in four of the next five days. Romney adviser Charlie Black said the Republican’s rise to even with Obama, and even leading, in national polls suggests naturally that he has closed on Obama in Ohio, too.

“I promise you, he’s back in the game in Ohio,” Black said.

A Republican familiar with some of Romney’s polling says internal polls before last Wednesday showed Obama with 5-point leads in Ohio and Virginia. In Ohio, Romney was winning in conservative congressional districts before the debate, but only by 1 or 2 percentage points instead of the 5 or 6 points he would need to carry the state. But post-debate, Romney has opened a 5-point lead in those districts in internal polling, according to the Republican who spoke on condition of anonymity without authorization to publicly discuss the polls.

Republican vice presidential nominee Paul Ryan and Vice President Joe Biden were preparing to take the debate stage Thursday in Kentucky. Romney and Obama have two more debates this month.

Obama’s aides said the president was upbeat in private, looking for another shot to do better in an Oct. 16 debate in New York. The president has held no formal practice sessions with sparring partner Sen. John Kerry, D-Mass., since the first debate. Instead, Obama and Kerry — who is playing the role of Romney — separately have been studying the positions the Republican nominee outlined in the debate and how they differ from where he stood earlier in the campaign.

The president, Kerry and the Democratic debate team will head to Williamsburg, Va., this weekend for intensive preparations before next Tuesday’s face-off at Hofstra University in Hempstead, N.Y. They held a similar “debate camp” in Nevada in the days before the first debate.

Obama plans to rally support from students at Ohio State University today, the last day for Ohioans to register to vote. Early voting is under way there and in many other states in one form or another.

Romney is set to promote his farming policies in Iowa and then Ohio. Tough-talking New Jersey Gov. Chris Christie was joining Romney for a second day of Ohio campaigning Wednesday. Ryan lamented the negative ads from Obama’s campaign blanketing the Ohio airways.

“He doesn’t have anything to run on so he’s running all of these ads, outspending us here in Ohio trying to basically call us liars,” Ryan told WTOL, a TV station in Toledo, Ohio.

The Obama campaign unleashed a new ad today on national broadcast and cable networks featuring its favorite new weapon: Big Bird.

Employing ominous narration, the spot ridicules Romney for singling out the “Sesame Street” character and PBS subsidies as examples of spending he would cut. “One man has the guts to say his name,” says the ad, which flashes to Romney and then the feathered creature. “Big. Yellow. A menace to our economy. Mitt Romney knows it’s not Wall Street you have to worry about. It’s Sesame Street.”

The Romney campaign ridiculed Obama’s campaign for focusing on Big Bird instead of serious issues. Romney spokeswoman Amanda Henneberg pointed to Obama’s speech accepting the Democratic nomination in 2008, when he said: “If you don’t have a record to run on, then you paint your opponent as someone people should run from. You make a big election about small things.”

“With 23 million people struggling for work, incomes falling, and gas prices soaring, Americans deserve more from their president,” Henneberg said in a statement.

Pickler reported from Washington. Associated Press writers Jim Kuhnhenn, David Espo and Julie Pace in Washington, Tom Beaumont in Des Moines, Iowa; Steve Peoples in Newport News, Va.; and Ann Sanner in Columbus, Ohio, contributed to this report.