After a strong debate performance, Republican challenger Mitt Romney is intensifying his efforts in the state that's critical to his White House hopes, while President Obama works to hang on to the polling edge he's had here for weeks.

Both candidates campaigned hard in the state Tuesday, the last day of voter registration ahead of Election Day, now just four weeks away.

"It's time for him to leave the White House," Romney said of Obama at an evening rally in Cuyahoga Falls. "Ohio's going to elect me the next president of the United States."

Obama, in Columbus, called out, "All right, Buckeyes, we need you." His campaign had buses nearby, ready to ferry students or other supporters to registration centers.

As Obama wooed Ohio State University students here and Romney focused on the Democratic bastion of Cuyahoga County to the north, there were signs the president's Ohio advantage was narrowing. A new CNN poll showed Obama leading Romney 51 percent to 47 percent among likely Ohio voters. And Republican strategists familiar with Romney's internal polling contended the race was even closer -- within a single percentage point -- as the candidate enjoyed a post-debate surge of support.

"I promise you he's back in the game in Ohio," said Charlie Black, an informal Romney campaign adviser.

Like other Republicans, he credits Romney's strong debate appearance last week as the reason for an uptick in national polling. And Romney advisers maintain they're seeing evidence of that in the battleground states most likely to decide the election, Ohio among them.

"There isn't any question that he has breathed new life and new energy into the Republican Party," Ohio Gov. John Kasich said Tuesday on a conference call with reporters. "We're seeing that there is greater intensity among Republicans and a great willingness to get out and vote and participate than we're seeing with Democrats."

With a hefty 18 electoral votes, Ohio is such a key state for Romney that one top adviser has dubbed it "the ball game" as the Republican looks to string together enough state victories to amass the 270 Electoral College votes needed to take the White House. No Republican has won the presidency without this Midwestern state, and if Romney were to lose here, he would have to carry every other battleground state except tiny New Hampshire.

Romney has far fewer state-by-state paths to the White House than Obama, who still has several routes to victory should he lose here.

Given the stakes and with just 28 days left in the campaign, Romney's schedule highlights his increased focus on the state: He's spending four of the next five days in Ohio, ahead of the second presidential debate in New York next Tuesday. Running mate Paul Ryan squares off against Vice President Joe Biden on Thursday for the sole debate featuring the No. 2s on the tickets.

Obama was being greeted in Columbus -- for a rally at Ohio State University -- by enormous letters that spelled out "vote early," a plea to the young voters who buoyed the president's bid in 2008. He arrived from the West Coast, where he had been raising millions of dollars for the campaign.

Obama campaign spokeswoman Jen Psaki dismissed the impact of polls showing a tighter race, saying Democrats always expected the race here and elsewhere to tighten ahead of Election Day.

Illustrating the competitive nature of Ohio, no presidential battleground has been more saturated with television advertising.

The campaigns and outside groups had spent more than $141 million on TV ads in Ohio through the beginning of October, one of the highest per-person spending rates in the country. Only more-populous Florida, which has seen $150 million in ad spending, has seen a higher total.

Ads in Ohio have focused on the energy industry -- some rural, southern areas of the state rely heavily on coal -- and on China, where foreign companies are seen as competing with Ohio's manufacturing base and jeopardizing jobs.

Obama has sought to paint Romney as a plutocrat who outsourced jobs during his tenure leading the private equity firm Bain Capital.

Romney, in turn, has sharply criticized Obama's support for stricter regulations on coal and natural gas. It's seen as a way in with white working-class voters, on which his candidacy depends. "Stop the War on Coal. Fire Obama," read signs that dot the countryside of areas where Romney has held multiple events.

White blue-collar workers prefer Romney to Obama, but less so than they did Republican George W. Bush, who carried Ohio in 2004. These voters are considered still persuadable, although Romney may have hurt himself with his comment that the 47 percent of Americans who pay no income tax believe they are victims entitled to government help.

Romney's position on the auto bailout also dogs him in a state that's heavily reliant on the industry. Obama's decision to offer government support to automakers meant protection for thousands of jobs at parts and supply companies in Ohio.

Romney wrote a 2008 op-ed headlined "Let Detroit Go Bankrupt," which has become a rallying cry for Democrats. They have argued Obama's support for the bailout has had a hand in Ohio's drop in unemployment, which is now lower than the national average.

In the final weeks, both campaigns insist they have the edge in the critical ground game. That battle was playing out in the courts, as well, with Ohio's election chief saying Tuesday he will appeal a ruling that reinstates the final three early voting days in the state.

Ohio Secretary of State Jon Husted called a decision last week by a federal appeals court "an unprecedented intrusion" into how states run elections.

Husted said Friday's decision by the 6th U.S. Circuit Court of Appeals would affect how elections are run in all 50 states. The appeals court in Cincinnati affirmed a lower court ruling and returned discretion to set hours on the final three days to local boards of elections.