Newt Gingrich’s attempt to offer a “nuanced” policy on illegal immigration in Tuesday’s GOP presidential debate may have exposed his Achille’s heel, and the former House Speaker’s Republican rivals are seeking to take advantage of that perceived vulnerability.

Minnesota Rep. Michele Bachmann offered what she called “more evidence indicating that Newt Gingrich is the most liberal GOP candidate,” in a press release that cites a pro-amnesty letter Gingrich signed in 2004.

The Gingrich letter, sponsored by the neoconservative National Foundation for American Policy (NFAP), called for President Bush to offer a “new path” via guest-worker arrangements and to “recognize that those already working here outside the law are unlikely to leave.” The letter was co-authored by longtime pro-immigration activist Tamar Jacoby and originally published Feb. 6, 2004, in the Wall Street Journal.

“This letter is a clear indication that Speaker Gingrich has a deep history of supporting amnesty,” Bachmann said in the press release, sent to national media Saturday. “I don’t agree that you should make 11 million workers legal because that in effect is amnesty and will only encourage more illegal immigrants to come here.”

Another Gingrich rival, former Massachusetts Gov. Mitt Romney slammed Gingrich’s proposal as amnesty, as did influential Iowa Republican Rep. Steve King.

After Tuesday’s debate sponsored by the Heritage Foundation and American Enterprise Institute, The American Spectator‘s George Neumayr criticized Gingrich for his “scolding tone” on immigration, saying that Gingrich had “alienated conservatives … with his holier-than-thou approach to illegal immigration.” Tim Albrecht, spokesman for Iowa’s Republican Gov. Terry Brandstad, said on Twitter after the debate: “Newt did himself significant harm tonight on immigration among caucus and primary voters.”

Roy Beck of Numbers USA, a group that advocates for lower immigration levels, said voters won’t like Gingrich’s “long-term record” on immigration.

“In fact, Gingrich’s leadership in Congress is one of the reasons we have so many illegal aliens today who have been able to stay in this country for 25 years,” Beck said in an online column Wednesday. “That’s the supreme irony of Gingrich’s pro-amnesty remarks in last night’s debate. The man who helped ensure that illegal aliens from the 1980s and 1990s are still here in 2011 asked voters last night to consider the inhumanity of making illegal aliens leave this country after they have sunk such long roots here.”

Beck noted that Gingrich had a career grade of “D” on Numbers USA’s report card on immigration issues.