VANDALIA, Ohio — Fresh from two policy speeches in New York, Republican Mitt Romney on Tuesday turned his attention to Ohio, a state pivotal to his presidential prospects and where polls show him running behind.

Romney joined with running mate Paul Ryan Tuesday afternoon to start a two-day bus tour in the battleground state after his speeches earlier on foreign policy — in which he bashed President Barack Obama on the Middle East — and education.

Obama, who spoke to the United Nations Tuesday and — like Romney — addressed a global conference sponsored by President Bill Clinton in New York, also campaigns in Ohio today in a sign of the state’s importance in the Nov. 6 election.

Romney at his rally described the vote as a referendum on “the soul” of America. “We cannot afford for more years of Barack Obama” he told more than 3,500 people gathered outside an airport hangar in Vandalia. “We’re not going to have four more years of Barack Obama.”

Romney is ramping up his schedule of public rallies this week as he tries to beat back complaints from some Republican leaders concerned he has been spending too much time raising money and not enough talking to voters. He has three campaign events scheduled Wednesday in Ohio.

His bus tour came as a Washington Post poll showed Obama leading him in the state, 52 percent to 44 percent. After Florida, Ohio is the second-largest state among the 10 or so that strategists from both parties say will decide the election.

No Republican has ever won the White House without carrying Ohio, which has 18 of the 270 Electoral College votes needed to win the White House.

Obama, Romney and their allies aired more than 29,000 ads on Ohio television stations in the 30-day period ended Sept. 17, the most in any state. The Post survey showed 36 percent of all Ohio voters say they’ve been contacted by the Obama campaign, while 29 percent said that of the Romney operation.

Romney, as part of an attack on Obama’s economic record at the Ohio rally, said the President has been too lenient dealing with China on trade issues.

“When people cheat, that kills jobs,” Romney said. “China has cheated. I will not allow that to continue.”

Romney’s campaign website site says that one of five executive orders he would issue on his first day in the White House would direct the Treasury Department to list China as a currency manipulator.

The Obama administration last week filed a challenge at the World Trade Organization accusing China of illegally subsidizing exports of automobiles and auto parts. The complaint was filed the day Obama campaigned in Ohio.

Besides Ryan, speakers at the Romney rally included Sen. Rob Portman of Ohio, who was a contender for vice president on the Republican ticket, and Sen. Rand Paul of Kentucky, a Republican popular among the anti-tax tea party movement.

Ryan continued a Republican attack on Obama for a comment by the President last week that “you can’t change Washington from the inside” and that the pressure to transform the capital’s political environment needs to come from the outside.

“If he can’t change Washington, we need to change Presidents,” Ryan said.

Rich Beeson, Romney’s political director, expressed confidence about his candidate’s prospects in Ohio. “We trust our internal polls,” he told reporters on Romney’s campaign plane on the trip to Ohio. “I don’t make any campaign decisions based on what I read in the Washington Post.”

Beeson declined to say what the campaign’s internal polling showed in the state. He also tried to dismiss questions about whether Romney has any victory path that doesn’t include Ohio.

“It’s like kids out there,” he said of campaign calculations. “You’re not ever going to say you’re going to lose one of my kids. So, it’s a nice wide-open path.”

Beeson said Obama’s campaign is displaying excess confidence, like a football player who celebrates before crossing into the end-zone for a score.

“They are sort of spiking the ball at the 30-yard line right now,” he said. “There are still 42 days to go. We are, by any stretch, inside the margin of error in Ohio.”

Earlier Tuesday, Romney urged more accountability for U.S. aid to other nations and greater reliance on free enterprise to lift the world’s poor toward prosperity.

“The aim of a much larger share of our aid must be the promotion of work and the fostering of free enterprise,” he said in his speech at the annual meeting of the Clinton Global Initiative in New York.

The appearance marked a moment of bipartisanship, given that Clinton’s prime-time speech at Democratic National Convention detailed the party’s case against Romney and that the former President has aggressively campaigned for Obama.

In his opening remarks, Romney joked about the impact of Clinton’s convention speech earlier this month.

“If there is one thing we’ve learned in this election season, by the way, it is that a few words from Bill Clinton can do a man a lot of good,” Romney said. “All I’ve got to do now is wait a couple days, to wait for that bounce to happen.”

Romney also used the address to spotlight turmoil in the Middle East, repeating a line of attack he’s taken against Obama this week.

“Syria has witnessed the killing of tens of thousands of people,” he said. “The president of Egypt is a member of the Muslim Brotherhood. Our ambassador to Libya was assassinated in a terrorist attack. Iran is moving toward nuclear weapons capability. We somehow feel that we are at the mercy of events, rather than shaping events.”

Obama in his address to the U.N. General Assembly pledged to world leaders that the U.S. will do what is necessary to block Iran from building a nuclear weapon. He also said that time for a diplomatic resolution to the Iranian issue “is not unlimited.”

Romney, after his appearance at the Clinton forum, took questions at an education forum sponsored at the New York Public Library by NBC News and various foundations. Asked about this month’s Chicago teacher’s strike, Romney said he wouldn’t like to see such actions blocked, calling them “a right that exists in this country.”

The former Massachusetts governor also said teacher compensation should be linked to student performance and preparedness. He reiterated his support for an expansion of school choice and for requiring states to give disadvantaged students access to any school, public or private.

On whether every child in America deserves the kind of private education Romney enjoyed in suburban Detroit, he said that isn’t possible and wouldn’t guarantee results.

“There are teachers in the public system that are every bit as good as those that are in the private system” he said. “I reject the idea that everybody has to have a, if you will, Harvard-expense level degree to be successful.”

At the college level, Romney has proposed a reintroduction of private banks to the student loan market, a move that would upend a central component of Obama’s education plan. College tuition rates are on an “unsustainable path,” he said.

Lis Smith, an Obama reelection spokeswoman, said in a statement that Romney’s rhetoric didn’t square with his record.

“We saw his education policies in action in Massachusetts, where he inherited one of the top school systems in the nation, and proceeded to make deep cuts in his first year that led to larger class sizes and higher college costs,” she said.