"He's trying to sound like a conservative but actually he sounds more like the 30-year establishment Washington insider that he is," Bachmann told reporters after attending church in Fort Dodge, Iowa.
Earlier in the day, Gingrich said on "Face the Nation" that his firm was paid the money by Freddie Mac but that he received only a small portion.
Bachmann, a congresswoman from Minnesota, said Gingrich, a former House speaker, needed to disclose more about the pay.
"We don't know how much that money is. It could be more than the average salary for Iowans," she said. "I call on Speaker Gingrich to give that money back to the American people.… While the rest of the country was dealing with economic meltdown, he was pocketing $1.6 million."
She contrasted Gingrich's consulting for Freddie Mac with her work at the time in Congress.
"I was working feverishly and actively to put Freddie Mac into receivership, which is bankruptcy," Bachmann said.
She reiterated her criticism that Gingrich and Mitt Romney were indistinguishable and not true conservatives, and she said that if she were elected president, she would follow the legacy of President Reagan and former British Prime Minister Margaret Thatcher.
"What differentiates me from all of the candidates in this race is the fact that I am the true proven tested constitutional conservative in this race," she said. "I'm not a convenient conservative. I'm not a pretend conservative and I'm certainly not a frugal socialist like we've seen with Newt-Romney."
Bachmann made the remarks on the third day of a bus tour of all of Iowa's 99 counties, an effort to reignite her sputtering campaign. Bachmann soared in the polls after she entered the race in June and won the Iowa straw poll, a key early test of organizational strength, in August. But her support has plummeted since then.
Bachmann said 60% of Iowans remain undecided, and she was confident she would regain their support.
"I think people are going to come back to their first love that they had back in the Iowa straw poll," she said.