Amid new polls showing Michele Bachmann far behind the leaders in the GOP nominating race, the Minnesota presidential hopeful showed no signs of losing heart Sunday on ABC's "This Week" with Christiane Amanpour. "We're doing exactly what we need to do," Bachmann said. "We're looking forward to Jan. 3" (the date of the Iowa caucuses). This came as a Des Moines Register showed her polling at 8 percent in Iowa, down from 22 percent two months ago. She's now in fourth place behind Herman Cain (23 percent), Mitt Romney (22 percent) and Ron Paul (12 percent). One bright spot: Her main Tea Party rival, Gov. Rick Perry of Texas, logged in at 7 percent, tied with Newt Gingrich. Despite her expressions of confidence, Bachmann repeatedly dodged Amanpour's questions about whether Iowa, as some of the congresswoman's own top aides have said, is a must-win state for her. "We're focused on it as we are on all the states," Bachmann demured. There were other miscues in Sunday's 13-minute outing on national TV. Bachmann said she "wrote the bill to repeal Obamacare." While she did author such a bill, the bill that eventually passed the Republican-led U.S. House was authored by Majority Leader Eric Cantor of Virginia. She remained steadfast in her criticism of President Obama's involvement in NATO's mission to help the rebels who just killed Libyan leader Muammar Gaddafi. "The last chapter isn't written," she warned. But she had to backtrack from her recent claim on illegal immigration, where she said that "59,000, alone this year, came across the border…from Yemen, from Syria… nations that are state sponsors of terrorism." Yemen has not been classified as a state sponsor of terrorism (as Bachmann had to acknowledge on ABC), and the Border Patrol report she cited was referring to the total number of illegal immigrants apprehended from countries other than Mexico. Of those, only 663 had ties to countries with links to terrorism, and only a handful of those came from Yemen or Syria. (Amanpour's figures, not disputed by Bachmann on-air: 11 from Yemen; 5 from Syria). Nevertheless, Bachmann said, even one is too many and her critics are "missing the point" about larger problem of border security. Amanpour also pressed Bachmann on her claim that Perry took her proposal for flattening the tax rates, an idea that's been around in GOP circles for decades. In fact, Perry's plan is quite different from Bachmann's. He'd give taxpayers the option of a single 20-percent rate, while Bachmann would abolish the entire tax code and replace it with several unspecified "flatter" but not flat tax rates. The other hallmark of Bachmann's tax plan is that, despite her general aversion to tax increases, she would make everybody pay up, including the roughly half of Americans who currently don't earn enough to pay a federal income tax. "Everyone needs to pay something," she said.