Despite polls that show she and Sen. John McCain trail the Democratic team of Sens. Barack Obama and Joe Biden -- and reports of tension between her and McCain -- Palin remains outwardly upbeat.
She told Vargas she is "thinking that it's going to go our way Tuesday, Nov. 4. I truly believe that the wisdom of the people will be revealed that day."
Asked about 2012, and whether she was discouraged by the daily attacks on the campaign trail and would instead pack it in and return to her home state of Alaska, she said:
"I think that if I were to give up and wave a white flag of surrender against some of the political shots that we've taken, that would bring this whole & I'm not doing this for naught," Palin said.
The woman who depicted herself as a pitbull with lipstick during her speech at the Republican National Convention claimed that much of the media's and her opponents' treatment of her had been sexist.
Particularly hurtful, she said, were vulgar T-shirts worn by detractors at several events.
"I was disappointed that my kids had to see that," Palin told Vargas. She said her 14-year-old daughter saw a man wearing one of the shirts that was "pretty appalling."
"And she said, 'Mom, how can that guy say that about you? He's never even met you,'" Palin said.
She said questions about her wardrobe and whether she could be vice president and raise a family at the same time were questions never asked of male candidates.
Palin shrugged it off and said the "double standard" made her more determined to "work that much harder for the women in America to show them that that final, hard-as-glass ceiling must be broken."
Despite her feminist rhetoric, Palin's support among women voters has fallen to about 40 percent, according to recent polls.
When asked why women aren't rallying to her, Palin said, "I don't look at polls, so I would not be able to answer that.
"But you have to consider that there has been the constant barrage, a kind of spin on the my record or my positions," Palin said. "Perhaps it would change someone's perception."
Undaunted, she vowed, "I'm not going to let the women of America down,"
Palin was equally at a loss to explain why people, including several prominent Republicans, such as former Secretary of State Colin Powell, claim she is unqualified to be vice president.
"I don't know," she said. "But there have been many underestimated persons who've been elected to office, and have really been then, provided the opportunity to prove the pundits wrong."
Palin was unapologetic about her attacks on Obama and his relationship to 1960s radical Bill Ayers, and Wednesday she linked Obama to Rashid Khalidi, a Columbia University professor and former PLO associate. Palin has also accused the Democrat of promoting socialism.
Vargas asked Palin if she continued to refer to Obama's relationships in order to suggest he was "un-American," an historically loaded term.
Palin said she was not calling Obama "un-American" but was calling attention to his record.
"[I'm] not calling him un-American. There is nothing wrong, though, with calling someone out on their record, their associations," she said. "The association issue here, it's not mean-spirited. It's not negative campaigning. It's important and fair to the electorate."
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