WASHINGTON -- The Obama campaign’s relentless effort to paint Mitt Romney as a dishonest, soulless snob is a risky strategy.

For months, Democrats have been running ads and issuing statements with the same, persistent themes: Romney’s pushing a tax cut plan that would send the already huge national debt soaring, while making the rich richer. He’s hiding something in the tax returns he won’t release. He doesn’t care about the middle class or the needy.

For this kind of offensive to succeed – and it sometimes does – Romney has to fit the image when most of the public finally pays attention. If not, the tactic boomerangs, and the aggressor can look mean and less presidential.

So far, polls show the affable Romney has benefited because he didn’t fit the scary profile when an estimated 67 million people watched the Oct. 3 presidential debate. The former Massachusetts governor’s favorability hit 50 percent in an Oct. 4-7 Pew Research Center poll, up 5 percentage points since last month, while Obama’s rating fell 6 percentage points, to 49 percent.

But the Obama campaign has persisted.

Saturday, its ad called Romney’s tax cut claims “dishonest.”

Sunday, Obama spokeswoman Lis Smith asked, “What does Mitt Romney have against the truth?” after the GOP nominee spoke in Florida.

Tuesday, the beat went on. “Mitt Romney looked straight into the crowd tonight and told downright falsehoods,” said Obama campaign spokesman Danny Kanner after a Romney speech in Ohio.

Wednesday, following a Romney appearance in Mount Vernon, Ohio, Kanner called the remarks “a barrage of head-spinning falsehoods.”

Despite his gains last week, Romney’s favorability rating is not all that high, and Pew said that only 39 percent found the Republican “honest and truthful.”

Demonizing does sometimes work, even for an incumbent president.

“We did quite a number on John Kerry,” said Curt Anderson, a veteran Republican strategist, recalling the negative campaign in 2004 when the Democratic senator from Massachusetts was the party’s standard-bearer.

The anti-Kerry group, Swift Boat Veterans for Truth, raised questions about his Vietnam War service. But Kerry, said Anderson, forgot another rule of political combat. “You win elections by effective counterpunching,” he said.

Romney is fighting back. He says his tax plan would not cost $5 trillion over 10 years, as the Obama campaign insists – an assertion hard to prove or disprove, since Romney won’t provide more specifics.

The independent Tax Policy Center said the plan would cost about $480 billion in 2015. But, it added, “Because Gov. Romney has not specified how he would increase the tax base, it is impossible to determine how the plan would affect federal tax revenues or the distribution of the tax burden.”

Romney is also counterpunching by raising questions about the administration’s handling of the crisis in Libya, where four Americans died, including the U.S. ambassador.

An email released earlier this week said the State Department withdrew U.S. security personnel from Libya just weeks before suspected Islamist extremists attacked the American consulate, despite warnings from the U.S. Embassy that the Libyan government could not protect foreign diplomats.