MOUNT VERNON, Iowa — Fresh off his more animated debate performance, President Obama joked Wednesday that he is still trying to get the hang of the face-to-face showdowns with Mitt Romney, even as the Republican nominee said Mr. Obama appears to be “running on fumes” in the run-up to Nov. 6.

Continuing the fierce line of attack he began Tuesday night, Mr. Obama told a rally in Iowa that Mr. Romney’s tax plans for the country are too “sketchy” for voters to risk putting him in the White House.

“Gov. Romney has been running around talking about his five-point plan for the economy for quite some time. And as I pointed out last night, and you guys heard yourselves, it’s really a one-point plan. … It says folks at the very top can play by their own set of rules,” Mr. Obama said, playing to big crowds in Iowa and later in Ohio, where 14,000 turned out to see him.

He and Mr. Romney picked up right where they left off in Tuesday’s town-hall-style debate, trading barbs on who would be worse for women over the next four years — Mr. Obama said the Republican would threaten access to contraception, abortion and women’s health care, while Mr. Romney said the president has ruined women’s economic prospects — and on energy and taxes.

Instant polls suggested Mr. Obama won Tuesday’s debate, though not by the overwhelming margins Mr. Romney notched in their Oct. 3 debate in Denver, which helped reset the race and propel the Republican to a lead in national polling.

Democrats were energized by the president’s debate performance, praising him for finally taking a hard line against Mr. Romney.

But the Obama campaign is still struggling to reset the post-Oct. 3 debate storyline that it is struggling in some of the key states.

Spokeswoman Jen Psaki on Wednesday vowed that the campaign won’t give up on Florida, North Carolina and Virginia — states where Mr. Romney has taken the lead in polls.

“The same states that were in play and that we’re competing in every single day are the same states today as they were three weeks ago,” she said.

On the other side, The Associated Press reported that the Romney campaign is so certain of victory in North Carolina it is considering pulling resources out of that state and sending them to Wisconsin, Pennsylvania or Michigan, to try to make a play for one of those states.

Mr. Romney spent the day campaigning in Virginia in Chesapeake and Leesburg, where he said the president didn’t present any plans for the next four years during the debate, but instead spent his time trying to tear down Republicans.

“He’s pretty much running on fumes, and the American people want some real answers, and a real agenda,” Mr. Romney said at an outdoor rally at Tidewater Community College.

Mr. Romney appeared at both Virginia rallies with Dennis Miller, who took a couple of biting shots at Vice President Joseph R. Biden.

“Biden never shuts up — it’s just occasionally you have to hood him like a falcon so you can get some sleep at night,” Mr. Miller said, before going on to compare people who voted for Mr. Obama to someone who took a sleeping drug and did things they now regret.

He then went on to deliver a testimonial to the Republican candidate himself, saying he has shown he can turn around the country.

“There’s an innate decency about this cat,” Mr. Miller said. “You do hear the word ‘gosh’ come out of his pie hole.”

He then acknowledged to the crowd in Leesburg that he was trying to stall for time because he had forgotten the last name of the next speaker, Rep. Frank R. Wolf, the longtime Republican representative from the region.

Tuesday’s debate featured the two men going toe to toe — literally — on many of the big issues of the campaign, including energy policy, taxes and last month’s terrorist assault on the U.S. Consulate in Benghazi, Libya, which left four Americans dead.

Mr. Romney appeared to stumble when he questioned whether the president had mentioned terrorism in his initial post-Libya speech in the Rose Garden. Mr. Romney said the administration was slow to spot what all sides now say was a terrorist assault.

In fact, Mr. Obama had mentioned “acts of terror” in that speech, though not specifically about the Libya attack. He and his administration spent much time in the days after the attack, including Mr. Obama himself in a speech to the United Nations, blaming an anti-Islam video.

On Wednesday, Ms. Psaki, his campaign spokeswoman, said that moment “exposed” Mr. Romney “as the guy who wanted to use Libya, use the tragic events overseas, as a political football.”

At his rallies, though, Mr. Romney did not address Libya, instead focusing on his domestic message and continuing his recent practice of trying to personalize his message.

The two men meet for one more debate Monday in Florida, with the focus squarely on foreign policy.

• Stephen Dinan reported from Chesapeake, Va.

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