Obama aides dispute much of the criticism of their tactics, pointing to their rapid response to Romney's apparent shift on abortion.
"We're not saying he's changed his mind on these issues," said Stephanie Cutter, Obama's deputy campaign manager. "We're saying he's trying to cover up his beliefs."
The president's support among female registered voters dropped 5 percentage points following the debate, according to Gallup surveys. But he still leads Romney 51 percent to 43 percent among women. The Republican's support among registered female voters is up 2 points since the debate.
Democratic pollster Stan Greenberg raised alarms this week about the potential for softening in Obama's support among women. He said his post-debate research found unmarried women in particular were not swayed by Obama's economic arguments but were open to Romney's approach.
"There was a positive response of these voters to Romney identifying with the middle class and their struggle and a very strong response to Romney's five-point economic plan," Greenberg said.
That marked a shift from last month, according to the pollster. Many unmarried women responded positively to Obama's message during the Democratic convention and were particularly offended by Romney's comments in a leaked fundraising video about 47 percent of voters who don't pay federal income tax and feel they are victims.
Obama never raised Romney's remarks during the debate, to the dismay of many Democrats.
The president's campaign did on Tuesday release its first ad since the debate incorporating Romney's comments on the 47 percent. The 30-second spot focused on seniors, arguing that some of the "victims" Romney referred to were seniors receiving Medicare.
Despite the Democratic worries, officials at Obama's Chicago campaign headquarters say their approach to the final weeks of the campaign has always hinged on a tight race.
"We never anticipated winning battleground states by 10 points and can't imagine winning a ton of them by 5 points," said Ben LaBolt, Obama's campaign spokesman. "Our task is to lay out the economic choice every day for undecideds and to turn out our supporters."
For some Democrats, who sensed some in the party getting overconfident before the debate, a case of the nerves may not be such a bad thing.
"I'd rather get a jolt four weeks out than a week out when there's still time to do something about this," said Karen Finney, a Democratic strategist.
Associated Press writer Ken Thomas and AP News Survey Specialist Dennis Junius contributed to this report.
Follow Julie Pace at http://twitter.com/jpaceDC
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