WASHINGTON — “Lead from behind” may be a sound bite the Obama administration regrets, but debating from behind is clearly something President Obama is very good at. He got the first debate’s wakeup call while Mitt Romney let the encounter in Denver mislead him into confusing petulance with strength.

For Obama’s supporters, the fact that the president played offense, had a strategy and seemed happy in his work was reason enough for elation. But the most electorally significant performance was Romney’s. Under pressure this time, the former Massachusetts governor displayed his least attractive sides. He engaged in pointless on-stage litigation of the debate rules. He repeatedly demonstrated his disrespect for both the president and Candy Crowley, the moderator. And Romney was just plain querulous when anyone dared question him about the gaping holes in his tax and budget plans.

Any high school debate coach would tell a student that declaring “believe me because I said so” is not an argument. Yet Romney confused biography with specificity and boasting with answering a straightforward inquiry. “Well of course they add up,” Romney insisted of his budget numbers. “I — I was — I was someone who ran businesses for 25 years, and balanced the budget. I ran the Olympics and balanced the budget.” Romney was saying: Trust me because I’m an important guy who has done important stuff. He gave his listeners no basis on which to verify the trust he demanded.

Romney’s stonewalling was so obvious that it opened the way for one of Obama’s most effective lines of the evening: “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 have taken such a sketchy deal. And neither should you, the American people, because the math doesn’t add up.” Obama sought to make that point in the last debate. This time he had a metaphor and a story to go with the arithmetic.

Romney also covertly disclosed that he, like George W. Bush before him, has every intention of cutting taxes on the rich. Like Bush, he used stealthy language to try to achieve a great fiscal cover-up.

Here was Romney on Tuesday: “I will not under any circumstances reduce the share that’s being paid by the highest-income taxpayers.” Here was Bush in 2000: “The facts are, after my plan, the wealthiest of Americans pay more taxes of the percentage of the whole than they do today.”

This really matters: Romney intends, as Bush did, to push for steep tax cuts for the wealthy. His only pledge is that he’ll keep the share of the total tax take paid by the wealthy unchanged, presumably by reducing other taxes too. And this is supposed to lead to lower deficits? How?

The most instructive contrast between Debate I and Debate II was the extent to which Romney’s ideas crumbled at the slightest contact with challenge. Romney and Paul Ryan are erecting a Potemkin Village designed to survive only until the polls close on Nov. 6. They cannot say directly that they really believe in slashing taxes on the rich and backing away from so much of what government does because they know that neither idea will sell. So they offer soothing language to the middle class, photo ops at homeless programs to convey compassion, and a steady stream of attacks on Obama aimed at shifting all the attention his way.

For his part, Obama looks strong when he calmly and methodically confronts the exceptionally large philosophical and practical differences that now divide the parties. He looks weak when he fuzzes up those differences in the hope of avoiding conflict. The fight is often asymmetric because Obama speaks for balance — between tax increases and spending cuts to reduce the deficit, between a thriving market and an active government — while today’s conservatives have no interest in balance.

In the first debate, Obama let Romney back into the race by failing to shake his opponent’s self-presentation. But Romney also put himself into contention by pretending to be a moderate, shelving his plutocratic side, and hiding his party’s long-term objectives.

In the second debate, the disguise fell. Romney revealed more of himself than he wanted to and asked voters to endorse a radical tax-cutting program without providing them the details that matter. Sketchy is one word for this. Deceptive is another.

E.J. Dionne’s email address is [email protected]