Here’s a thought experiment: Imagine where the presidential race would be if the Barack Obama of Debate Two had appeared at Debate One.

Obama entered the second of three rounds with many tasks to accomplish. He had to display vim and vigor—at least look as if he wants to be president and fight for that privilege. He had to offer a passionate defense—or explanation—of his presidency to date, outlining his accomplishments in what-it-means-for-you terms. He had to convince voters he has a strong idea of what he will do in the next four years to build on the improvements of the past four. He had to cast the election as a stark choice between this vision and Mitt Romney’s back-to-Bush intentions. And he had to call out the say-anything Romney on several fronts: being out of step (or touch) with the priorities and needs of middle- and working-class Americans, and refusing to own his policies and positions.

Romney had a much simpler task: repeat his charge that Obama has not done enough to bolster the economy and proclaim “I can do better.” Romney demonstrated in the first debate that he would not be burdened by any of his inconvenient or mathematically challenged stances. He could toss them aside, just like dumping a bad stock.

As I’ve noted before, this was always the fundamental dynamic of the race. Obama would have to explain (his record, his agenda, and his opponent), and Romney would merely have to stick to his mantra: This fellow had his shot, he came up short, and I’m the white knight riding to your rescue. Romney has had the easier path, and if recent polls are any indication, Romney, after months of cloddish campaigning and weeks of 47 percent troubles, finally succeeded in selling this proposition—hire me to be the CEO of the United States—at the first debate, especially to white women voters. His PowerPoint came home.

On Tuesday night, at the town-hall-style debate at Hofstra University, a fierce and passionate Obama put a dent in that presentation. He challenged Romney repeatedly: on Romney’s tax plan (whatever it may be), on Romney’s crass effort to politicize the attack on US diplomats in Libya, on Romney’s past investments in firms outsourcing in China. In one early exchange, Obama rolled Romney’s opposition to the auto bailout, his record at Bain Capital, and his proposed tax cuts for the wealthy into one answer—merging Romney’s various liabilities into a single, integrated assault. Four times Obama said to Romney, “That’s not true.” In one critical exchange, moderator Candy Crowley felt compelled to back up the president, when Obama challenged Romney’s assertion that it took him a fortnight to declare the Benghazi attack an act of terrorism. The president had labeled it as such the day afterward.

That was a low moment for Romney. Obama forcefully took on Romney’s charge that his administration had misled the nation about the Libya episode, declaring Romney’s claim “offensive.” The glare Obama aimed at Romney was devastating. The Republican presidential candidate seemed rattled and proceeded to deliver his usual national security shtick—Obama is weak, he apologizes for America, and his foreign policy is unraveling—in a tentative manner. In this back-and-forth, the only one concerning foreign policy, Obama came across as resolute. Romney at that moment seemed desperate.

For most of the debate, Romney essentially had one argument: I know how an economy works, I know how to create jobs. He said “I know how” several times. This is his bottom line, and he did deliver this pitch with confidence. After all, Romney first became a success in business as a consultant telling CEOs that he knew more about their companies than they did. Next, he became a smash in the private sector by convincing investors to hand his firm millions of dollars for various deals. He does know how to win over an audience—at least in a corporate boardroom. And he applied that skill masterfully in the first debate. Yet up against a reinvigorated Obama who pushed back constantly, Romney couldn’t make his case as easily as during the previous debate.

Pounding at Romney’s tax plan, Obama let some sarcasm and wit show: “If somebody came to you, Governor, with a plan that said, ‘Here, I want to spend $7 or $8 trillion, and then we’re going to pay for it, but we can’t tell you until maybe after the election how we’re going to do it,’ you wouldn’t take such a sketchy deal.” At another point, Obama derisively said of Romney: He “doesn’t have a five-point plan; he has a one-point plan. And that plan is to make sure that folks at the top play by a different set of rules.”

The two squabbled over assorted policy issues. Romney kept insisting Obama’s economic plan has failed. Obama slammed Romney for vowing to defund Planned Parenthood, for advocating self-deportation for undocumented immigrants, for flip-flopping on an assault weapon ban, and for aiming to voucherize Medicare. (He mentioned Romney’s attack on Planned Parenthood four times—obviously looking to shore up his support among women voters.) Romney, he said, has “gone to a more extreme place when it comes to social policy,” and the president obliquely assailed Romney for opposing abortion rights: “Gov. Romney feels comfortable having politicians in Washington decide the health care choices that women are making.”

The president stuck to his overall strategy, portraying the 2012 election as a clear choice in basic approaches. “What’s at stake in this election,” he noted, is “a fundamentally different vision about how we move our country forward.” And in a brilliant finale, Obama made this point in the concluding moments by referring to Romney’s 47 percent rant (see video clip below):

I believe Gov. Romney is a good man. Loves his family, cares about his faith. But I also believe that when he said behind closed doors that 47 percent of the country considered themselves victims who refuse personal responsibility, think about who he was talking about. Folks on Social Security who’ve worked all their lives. Veterans who’ve sacrificed for this country. Students who are out there trying to hopefully advance their own dreams, but also this country’s dreams. Soldiers who are overseas fighting for us right now. People who are working hard every day, paying payroll tax, gas taxes, but don’t make enough income. And I want to fight for them. That’s what I’ve been doing for the last four years. Because if they succeed, I believe the country succeeds.

This was Obama’s closing argument—and he dropped the 47 percent bomb when Romney would have no chance to respond. The former governor couldn’t apologize. He couldn’t explain. This was the last fact of the night, not a disputed talking point. (A senior Obama campaign aide tells me that the president’s late-in-the-debate deployment of the 47 percent ammo was not prearranged. Obama was “certainly prepared for it to come up if there was a good opportunity,” he said. “But questioners drove the timing. [We] couldn’t have planned that.”)

There’s no telling if Obama’s performance will have the same impact as Romney’s in the opening bout and cause a discernible shift in the polls. Assorted instapolls indicated Obama was the winner, especially among independent voters. But Romney’s basic appeal—I could do better reviving this sluggish economy—remains. And it’s not that tough to sell. Consequently, the basics of the contest have not changed. This is a close race. Water can slosh around in the bathtub, but it does return to its natural level. On Tuesday night, a turbo-charged Obama ensured the election would not spin out of his control—and that this will be a scratch-and-claw fight to the end.