“The president came over to me and said naming a person in the State Department would put them and their family at risk, which I perfectly understand,” he said. “He assured me he would bring the people responsible for that murder to justice. The way he looked me in the eye, I felt he really meant what he said.”

Mary Follano, who asked Mr. Romney if he would preserve tax deductions for mortgage interest and other breaks “important for the middle class,” also did not resolve her indecision.

Mr. Romney has pledged to pay for sweeping tax cuts by closing loopholes. At the debate, he suggested giving middle-income Americans a “bucket” of deductions worth a fixed amount. “I will not under any circumstances increase taxes on the middle class,” he said.

Mr. Obama called Mr. Romney’s proposal a “sketchy deal.”

“You have the governor saying, ‘Oh, yes, the numbers add up — I’ve been a businessman for years,’ ” Ms. Follano said. “You have the president saying they don’t add up.”

Ms. Follano, 54, a respiratory therapist with six grown children, some struggling with part-time jobs, said she agreed with Mr. Obama on raising taxes on incomes above $250,000. But she was sympathetic when Mr. Romney said raising taxes on high earners would hurt small-business owners, who create jobs.

“Normally I just go right in and vote Republican,” Ms. Follano said. If the election were today, she said, she might leave the line blank.

Phillip Tricolla, who works in construction, said he had entered the debate leaning toward Mr. Romney and exited the same way, but no firmer. Mr. Tricolla, 52, skeptically asked Mr. Obama why his energy secretary had said the government was not responsible for gas prices. He listened to the president reply that oil and gas drilling was the most extensive in years. But Mr. Tricolla agreed with Mr. Romney that the government should do more.