On the seal of the United States, the eagle turns its head toward its right talon, which holds an olive branch, and away from the talon holding 13 arrows. It is meant to suggest a preference for peace. The eagle that hovered between the two candidates in the second debate had the same design, but for one difference: The eagle's head was turned toward the arrows. It was a fitting symbol for the pointed and sniping contest between President Obama and Gov. Mitt Romney Tuesday night.

It was a night of barbs, interruptions and charges and countercharges. "Very little of what the president said is true," said Romney. "It's not true, governor," said Obama. "Not true. It's not true." During one exchange, Romney said, "You'll get your chance. I'm still speaking," as the audience in the arena seemed to gasp. At another point, the two men got so close and huffy, I thought moderator Candy Crowley might just ask them to take it outside.

It's a pretty good bet that undecided voters missed the important matter the guys were squabbling over. The debate was the only town hall-style contest in which voters posed questions. Just as the candidates seem to be speaking past the electorate, it often felt as if they were speaking past the questioners. Both candidates avoided answering questions about gas prices. Romney continued to show an aversion to specifics in explaining his tax plan, and the president didn't do a great job of answering a voter who wanted to know what Obama was going to do to earn his vote.

If you had to score a winner, you'd give the night to the president -- barely. He was a forceful advocate for his policies, kept Romney on defense and gave Democrats plenty to cheer. He probably stopped his slide in the polls. He looked like a person who would fight for the middle class.

But Romney showed that his first debate performance was no fluke. He consistently offered a confident alternative to the weak Obama recovery. "I can tell you that if you were to elect President Obama, you know what you're going to get," he said. "You're going to get a repeat of the last four years."

Each candidate accused the other of not telling the truth, and both offered examples of what that looks like. Romney told a false story about the past, and Obama told a false story about the present. During a politically charged exchange about fair pay for women, Romney recounted the early days of his Massachusetts administration.

"I had the chance to pull together a cabinet, and all the applicants seemed to be men," he said. And I -- and I went to my staff, and I said, 'How come all the people for these jobs are -- are all men?' They said, 'Well, these are the people that have the qualifications.' " In recounting how he went on a search for qualified female candidates, Romney remembered, "I went to a number of women's groups and said, 'Can you help us find folks,' and they brought us whole binders full of women."

On its face, the answer is odd. Romney sounds a little out of touch with the inequities of the workplace. The notion that women had to be scared up from the bushes seems from another era. But the main point for a candidate whose veracity is a key talking point for his opponent is that the story may not be true. The Boston Phoenix has fact-checked the story and claims that the binder of women was presented to Romney when he came into office. He didn't appear to ask for it, as he claimed in Tuesday night's debate. Perhaps he asked for another binder. In the end, however, as governor, Romney did hire a lot of women.

Romney was asked directly about how he was going to pay for his tax plan, and his answer was no better than it has been for months. He named no loopholes he would close but offered the faux-specificity of a $25,000 cap on deductions. This is a very small piece of specificity in explaining how he would pay for a $5 trillion tax cut.

The president's tall tales came during a debate over Libya. The administration's story is changing almost daily about what happened, who knew what when, and who is going to take responsibility for it. The topic presents political peril for the president. He effectively took command, saying that all responsibility rested with him and that he would get to the bottom of who killed the four Americans, including the ambassador. He criticized Romney for using the issue to score political points and took umbrage at the suggestion that anyone in his administration would act politically.

Then, he proceeded to act politically. That is, if you define acting politically as suggesting something that isn't true is true for the purpose of saving your job.

Obama said, "The day after the attack, governor, I stood in the Rose Garden and I told the American people ... that this was an act of terror." Obama was trying to suggest that he had declared this a terrorist attack long before his administration actually did. For days and days afterward, administration officials would not claim it was a terrorist attack.

U.N. Ambassador Susan Rice famously refused to call it such on "Face the Nation." The president was trying to reset the timeline. If you look at the president's statement in the Rose Garden, he does use that phrase, but it's a throwaway cliché. Indeed, it arguably wasn't about the attack at all, just a bromide about more general acts of terror.

In any event, the president buried the lead in the tenth paragraph of his remarks. That's why none of the papers at the time reported that he had characterized any part of the attack as having to do with terrorism. When Romney called him on it, the president wouldn't answer. "Please proceed, governor," he said, as if he were the moderator and not the fellow who was being called out. It was the verbal equivalent of putting your hands over your eyes and pretending no one will see you.

In the end, this picture of the debate says it all -- the two candidates pointing at each other in mid-sentence. The next debate is less than a week away. The topic will be foreign policy and national security. The eagle will hang between the two men there, too. But for that final debate, questions of war and peace will actually be central to the discussion, not just a fitting description of it.