Gingrich said in an interview with ABC News Thursday that although his opponents were welcome to take shots at him, he did not believe they would be effective.
One of the most common criticisms leveled against Massachusetts Gov. Romney by both Democrats and rival candidates is that he bases his decisions on political convenience. Bachmann continued this line of attack Thursday, saying he has been on "both sides" of issues important to voters.
"If you look at Mitt Romney, he has the same problem [as Gingrich], he's been very inconsistent on the issues. He's been on both sides of the abortion issue, on both sides of the issue for same-sex marriage," Bachmann said.
Romney fought back against this perception earlier this week, addressing for the first time the negative attacks on him by the Democratic National Committee and fellow GOP presidential contenders.
Critics frequently attack Romney by associating his healthcare reform in Massachusetts with President Obama's.
The healthcare issue is “by far the biggest challenge I have in the primary race,” Romney said on Fox News’ “Special Report” with Bret Baier. “If I were willing to say anything to get elected, wouldn't I just say, oh, it was a mistake.”
— Alicia M. Cohn and Justin Sink contributed to this report.