But not everything the candidates said during the high-stakes debate at Long Island's Hofstra University was concrete correct. Here's a fact check of some of what they said:
In response to the debate's first question, Romney said: "I want to make sure we keep our Pell Grant program growing. We're also going to have our own loan program, so that people are able to afford school."
Romney has argued that "a flood of federal dollars" is contributing to the increasing cost of higher education. In an education white paper he vowed not to "write a blank check to universities to reward their tuition increases." Romney's campaign said he would not reduce the maximum Pell Grant award of $5,550 a year.
Romney suggested early in the debate that he proposed bankruptcy for General Motors and Chrysler and that Obama pursued the plan Romney suggested. That's not correct. Obama pursued a structured bankruptcy for the automakers, one where details such as what unions and management would each give up, and what would happen to restructuring of the companies' debt, were worked out in advance. This assured the companies would enter and leave bankruptcy quickly, instead of a long, drawn-out proceeding that could have pulled many suppliers into bankruptcy, too.
Romney suggested that the lack of a clear energy policy is why gasoline prices are higher today than when Obama took office. Obama correctly noted that he came into office amid the deepest crisis since the Great Depression, one where demand for gasoline and oil plunged and took prices with it. Separately, however, there is plenty of evidence than the price of oil has increasingly been driven by factors having little to do with supply and demand, factors such as large-scale financial speculation, soaring oil prices because of fears of Middle East unrest and even the strength or weakness of the U.S. dollar.
Obama and Romney sparred over why the number of leases on federal land for oil and gas drilling have fallen. Obama correctly noted that he revamped the leasing program in an effort to force energy companies to use their leases or lose them. Curiously, the president did not mention the BP oil spill in the Gulf of Mexico. Much of the drilling on federal land is actually offshore, and much of the falloff in production came in the aftermath of the devastating oil spill, when the administration halted deepwater drilling and slowed shallow water activity in order to review safety procedures.
Romney challenged the Obama administration's varying accounts of the Sept. 11 attack on the U.S. consulate in the Libyan city of Benghazi.
He said that the president himself called it an act of terror in a Rose Garden statement the following day, and yet five days later, Susan Rice, the U.S. ambassador to the United Nations, called it a spontaneous assault prompted by an anti-Islamic video posted on YouTube. The first administration official to publicly call the assault a "terrorist attack" was Matthew Olsen, the director of the National Counterterrorism Center, during a Sept. 19 appearance before the Senate Committee on Homeland Security and Governmental Affairs.
Obama, without addressing the differences in the administration's accounts, agreed that he'd called the assault an act of terror in the Rose Garden, as did the moderator, Candy Crowley.
Yet the transcript of the statement shows that all three misspoke. Obama did not directly and specifically call the assault an act of terror.
Instead, he appeared to be speaking generically about how acts of terror wouldn't change the values of the country and its people:
"Our country is only as strong as the character of our people and the service of those both civilian and military who represent us around the globe. No acts of terror will ever shake the resolve of this great nation, alter that character, or eclipse the light of the values that we stand for."
The candidates argued over China, with Romney saying he would label China a currency manipulator on his first day in office. Doing so, he said, would allow him to impose penalties on Chinese goods. The penalties would actually be limited, and Democrats in the Senate have proposed a bill that would give the right to take tough actions to prod China. Candidate Obama in 2008 supported such legislation but as president did not push for it. What Romney did not say Tuesday is that such a move would also make imported goods more expensive, and China would be sure to retaliate against U.S. exports, which have grown sharply to China.
Obama, in defending his record on China, said tough actions on China have resulted in the Asian power allowing its currency to appreciate 11 percent. China has allowed its currency to appreciate, a process that followed a dialogue started under the Bush administration by then-Treasury Secretary Henry Paulson. Obama also suggested his pressure on China has resulted in more exports to China, which seems dubious since U.S. exports to China have grown steadily since China fully came under the umbrella of global trading rules in 2001.
Romney said Iran is four years closer to a nuclear bomb. Iran surmounted the most difficult facet of developing a nuclear weapon enriching uranium in high-speed centrifuges years before Obama became president. Moreover, the U.S. intelligence community said in a 2007 unclassified report that Iran stopped work on developing a nuclear warhead in 2003, but that it retained the ability to revive the effort.
"The U.S. intelligence community said with high confidence that Iran already has the scientific, technical and industrial capacity to produce nuclear weapons if it decides to do so. What that says is that basically there isn't a damn thing we can do aside from invading to stop them from getting a nuclear weapon if they decide to do so," said Greg Thielman, a former State Department intelligence analyst now with the Arms Control Association. "It's just a question of how long it would take them."
"Iran had the capability before Obama became president," he said, adding that Iran has shortened the time it would take to produce bomb-grade uranium since Obama took office. But, he said, Iran's stockpiles of low- and medium-enriched uranium are under constant monitoring by U.N. International Atomic Energy Agency inspectors and cameras.
"If they chose to break out, they would be completely exposed not for weeks, but months before they had the ability to threaten us with a nuclear weapon," said Thielman.
At the same time, Obama's strategy has not only failed to force Iran to halt uranium enrichment, but Tehran has continued expanding its enrichment capacity and refuses to answer U.N. questions about an alleged warhead development program.
Romney said that Obama failed to put forth an immigration overhaul plan in his first term. It's true that the Obama administration hasn't authored a specific immigration proposal, in large part because it knew that one wouldn't get through a Republican-controlled House of Representatives and would likely die a procedural death in the Senate. Obama did sign an executive order in June to stop deporting young illegal immigrants who came to the United States as children, if they meet certain requirements.
Romney has said he doesn't support the DREAM Act, a measure that would have allowed illegal immigrants under 30, who entered the United States before age 16 and lived in the country for five years without committing a serious crime, to be eligible for legal residency. However, Romney said he supports one provision in the act that allows a path to residency for illegal immigrants who serve in the U.S. military.
Obama charged that Romney embraced the controversial Arizona immigration law and called it "a model," but fact checkers have said that Romney at a Republican primary debate was referring to an earlier state law that required employers in the state to use the E-Verify system to determine whether someone is in the country legally, a point the Republican made in the debate.
Jonathan S. Landay, Lesley Clark and Kevin G. Hall contributed.