With swinging polls making the White House race as unpredictable as ever, President Barack Obama and Republican challenger Mitt Romney were crossing Ohio Tuesday 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 Tuesday 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.

Romney Adviser Kevin Madden said Romney will focus on plans to bring back manufacturing jobs in Ohio, drawing clear contrasts with Obama on issues that effect that sector such as energy, health care and tax reform.

"We still believe that this is going to be a campaign that is very close," Madden told reporters traveling aboard Romney's campaign plane. "But we do see a lot of enthusiasm from a lot of our core supporters and we see a lot of undecided voters that are taking a new look at Gov. Romney."

In Iowa, Romney appeared at a farm and outlined agricultural policy changes he would make, including tax relief for farmers and easing of environmental regulations that make it harder for them to do their job. He encouraged his supporters to find someone who voted for Obama four years ago and convince them to change their vote. "I need your help," Romney said.

Ryan, Biden to debate

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 on Tuesday, 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

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 Tuesday 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."

Sesame Workshop, the producer of the show, said in a statement on its Web site that it requested the ad be taken down because it's a nonpartisan nonprofit that doesn't participate in political campaigns.

Romney ridiculed Obama for focusing on Big Bird instead of serious issues. "So you have to scratch your head when the president spends the last week talking about saving Big Bird," Romney said told his Iowa supporters.