WESTERVILLE, Ohio — Scrambling to regain his footing in the Buckeye State, Mitt Romney enlisted the help Wednesday of a golf legend and a television star with the sort of blue-collar credentials that could resonate with the state’s working-class voters. President Obama, meanwhile, made his own Ohio pitch to college crowds at Bowling Green and Kent State.

The dueling visits spoke volumes about the critical role that Ohio — a state where manufacturing jobs in the automobile industry and other sectors have been lost in recent years as companies have shifted operations overseas — is expected to play in the coming presidential election.

Voters here have been pummeled with political television advertisements.

Bloomberg News reported this week that between the two campaigns and their supporters, there have been 29,000 ads aired here in the month before Sept. 17 — more than any other state in that time.

The ad blitz comes during a crucial stretch of the race, with both campaigns urging Ohioans to take advantage of state law that allows them to start early voting next week.

The stakes could not be higher for Mr. Romney: No Republican has won the presidency without Ohio, and the latest round of polling does not bode well for his chances of capturing the state come Election Day.

Mr. Romney kicked off his celebrity twofer by linking up with golf legend Jack Nicklaus, an Ohio native, at a campaign rally outside Columbus, and then teamed up with Mike Rowe, host of the Discovery Channel’s “Dirty Jobs,” at a business “roundtable” meeting in the Cleveland suburbs.

Mr. Romney used the stops and another in Toledo to warn that Mr. Obama will continue to saddle future generations with trillions in debt and to hammer the president for failing to crack down on China’s unfair trade practices.

“We’re going to crack down on China when they cheat. They’ve stolen our jobs. That’s got to stop,” Mr. Romney said at the event with Mr. Nicklaus, who told the crowd of about 2,000 that the former Massachusetts governor was the right man for the job.

Mr. Rowe did not endorse Mr. Romney, saying instead his experience on “Dirty Jobs” has taught him thatthe nation is disconnected with the plumbers, public works employees and tradesman that make “civilized life possible for the rest of us.” The reality TV star said a greater emphasis should be placed on promoting those professions as good jobs.

“I mean, there’s got to be a better way to be happy and successful in your career than simply assuming a massive amount of debt and exiting an educational program that gives you a degree without training,” he said.

The flash of star power could be just what the doctor ordered for the Romney campaign, as the appearances coincided with a new CBS/New York Times/ Quinnipiac University poll that held ominous signs for the Republican nominee in Ohio, as well as in Florida and Pennsylvania.

The survey found Mr. Obama holds a 53 percent to 43 percent edge over Mr. Romney among likely Ohio voters. Those surveyed also gave Mr. Obama a 6-point advantage when it comes to the economy — a month after the two candidates were even on the issue.

The poll came on the heels of a Washington Post survey released Tuesday that gave Mr. Obama an 8-point lead here. It also showed that more likely voters in Ohio trust the Democrat more when it comes to handling the economy and think he has a better understanding of the problems people are facing on the economic front.

Part of the problem for the Romney camp is that the improving employment picture in Ohio muddies the Republican candidate’s argument that Mr. Obama’s policies are suffocating job creation. That attack has put Ohio Gov. John Kasich, a Republican, in the tricky position of explaining the state’s success without undercutting Mr. Romney’s message.

“I hope you all know that Ohio’s coming back,” Mr. Kasich said Wednesday. “From 48th in job creation to No. 4. No. 1 in the Midwest. From 89 cents in a rainy-day fund to a half a million dollars, and we have grown 123,000 jobs in the state of Ohio. Our families are going back to work.”

He added, “But every day I have to face the headwinds that come from Washington.”

The Romney camp is downplaying the recent surveys, suggesting their internal polling numbers tell a different story.

“After the debates and after the campaigns and after all the ads are over, the people of Ohio are going to say loud and clear on Nov. 6, ‘We can’t afford four more years; we must do better,’” Mr. Romney said.

Mr. Obama countered Mr. Romney’s criticisms at the rally at Bowling Green State University, telling the young crowd that the Republican’s tough talk on China rings hollow.

“It sounds better than talking about all the years he spent profiting from companies that sent our jobs to China,” Mr. Obama said. “So, you know, when you hear this newfound outrage, when you see these ads he’s running promising to get tough on China, it feels a lot like that fox saying, ‘You know, we need more secure chicken coops.’”

Mr. Obama was referring to Mr. Romney’s $75,000 investment in CNOOC Ltd., the Chinese state-owned oil company, which was revealed when former Massachusetts governor released his 2011 tax return last week. Mr. Romney’s blind trust purchased the shares, then dumped them, Mr. Obama charges, when the presidential candidate decided he was going to start talking tough on China.

In the past week, Mr. Obama has repeatedly attacked Mr. Romney for the CNOOC investment, even after a report in BuzzFeed said the White House had applauded the Chinese company’s efforts to foster the development of carbon capture and storage in both countries.

⦁ Susan Crabtree reported from Washington.

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