WASHINGTON — This is presidential? They bicker, interrupt, talk over the moderator.

To some, the Obama-Romney rematch was squirm-inducing; but shedding some dignity probably won’t cost the candidates much. Since both President Barack Obama and challenger Mitt Romney came out swinging, neither was likely to claim a decisive advantage among viewers who thought the debate smacked of the wrong type of reality TV. And many backers who were already lined up on the two sides of the superheated race were looking for a scrappy face-off.

“In the world of ‘The Real Housewives,’ everybody needs to turn over a table from time to time,” said Evan Cornog, dean of the Communications School at Hofstra University, where Tuesday night’s debate took place. “How good that is for the republic, I don’t know.”

The presidency isn’t a person; it’s an institution. Americans traditionally expect presidents seeking re-election to maintain a certain level of decorum. Challengers get more leeway but still are expected to pay deference to the office of chief executive, if not to the man. Maybe that tradition is doomed in a conflict-addicted popular culture where even television cooking shows are “throwdowns.”

Can the notion of the dignity of office survive the era of flash analysis, when a phrase such as “binders full of women” launches a thousand Internet jokes — while the debate’s still in progress — and campaigns spin the matchup into attack ads within hours?

The tone of Tuesday’s faceoff was embraced by Democrats who were dismayed by Obama’s dreary performance in the first of this year’s three debates. They had urged him to adopt a more brass-knuckles style.

When Obama stepped up to meet Romney’s hard-charging persona, the result was a presidential campaign matchup that stands out as one of the most rancorous on live TV, especially for an event in which the candidates were onstage with everyday folks, fielding their earnest questions. Whether that was good or bad, it was one of the most exciting to watch.

Romney turned to the president and posed his own accusatory questions, demanding answers. When Romney made a point, Obama would shoot back, “Governor, that’s not true.” Six times he declared Romney’s words “not true.”

Maribeth McCarthy of Alexandria, Va., said watching the back-and-forth left her wishing that moderator Candy Crowley could bang a giant gong whenever someone fibbed.

“I don’t understand how it’s right for people to call each other liars on stage,” said McCarthy, a vice president at a financial institution, who said she expects to vote for Obama but wasn’t happy with either candidate in the debate. “How on Earth would we know who’s right?”

Texas A&M associate professor Jennifer Mercieca, who tuned in as part of her job, felt a similar distaste.

“Every time they would talk over each other or talk over the moderator, for me, it was cringe-worthy,” said Mercieca, who studies presidential communications. “It was unpleasant to see.”

Fidel “Butch” Montoya, a Denver pastor still mulling his vote, said the debate did seem less presidential but he liked watching the candidates “going face to face, nose to nose.”

“I enjoyed it because I think too often debates are cold, a waste of time,” said Montoya, who’s leaning toward Romney but waiting for the final debate to make up his mind.

Alan Schroeder, a journalism professor at Northeastern University who wrote a book on presidential debates, said plenty of them over the years have been downright dull — and this one was lively, even when it ran over the scheduled 90 minutes. So there’s nothing wrong with turning up the heat a bit, he suggests.

“I think debates should be entertaining,” he said. “It’s political theater.”

Debates traditionally are better at energizing a candidate’s supporters, at building voter turnout, than they are at changing minds or reaching the elusive undecided voters, Schroeder said.

In theory, Tuesday’s event was focused on the narrow sliver of undecideds. The questions came from among a pool of 82 voters chosen specifically because they still called themselves uncommitted to either candidate three weeks before Election Day.

“It was, for a town hall debate, particularly aggressive,” Schroeder said. “There’s always a risk involved in that; because the people in the audience are there to hear their questions answered, not to watch a struggle between the two candidates.”

However, Schroeder felt the candidates didn’t go too far: “It was sharp, but it was never out of bounds.”

The candidates made a point of looking their questioners in the eye, calling them by name and voicing sympathy for their concerns; but over and over, Obama or Romney quickly pivoted from addressing a voter to assailing the other fellow. Often they talked right through their time limits.

At one point Crowley implored Romney to shorten his answer: “Do you see all these people?” she said. “They’ve been waiting for you.”

At another moment — with Romney trying to make a point about investment in China by asking Obama over and again, “Have you looked at your pension?” — Crowley firmly asked the former Massachusetts governor to sit down.

It’s probably too early to say whether Tuesday’s show and the fiery vice presidential faceoff between Joe Biden and Paul Ryan might signal a more aggressive style of political debate for a coarsening American culture.

“What does this foretell?” Cornog asked. “Is it a trend? Or is it just an artifact of Romney’s Hail Mary pass in the first debate, and the president’s people deciding they have to match that strategy?”

Plenty of viewers found the event “too rude,” Cornog said, but there won’t be many consequences for Romney or Obama, so long as both are perceived as equal offenders.

“If you didn’t like it,” he said. “You really don’t have any place to go as a voter.”

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