Mitt Romney speaks as U.S. Sen. John Thune (R-S.D.) stands by during an appearance before employees at the Nationwide Insurance building November 23, 2011 in Des Moines, Iowa. (Mark Kegans/GETTY IMAGES)

Gingrich, a former House speaker who has surged in the polls to challenge Romney’s front-runner status, outlined in Tuesday night’s CNN debate what he called a “humane” immigration policy that would allow millions of undocumented immigrants who have settled in America and are raising families here to become legal residents. It’s a stance that threatens to hurt Gingrich’s standing with conservative activists, particularly here in Iowa, where the Jan. 3 caucuses kick off the nominating contest.

Romney, whose campaign efforts in Iowa are intensifying, said at a news conference here Wednesday that Gingrich’s proposal is “the wrong course for a Republican debate.”

“I just think we make a mistake as a Republican Party to try to describe which people who’ve come here illegally should be given amnesty to be able to jump ahead of the line of the people who have been waiting in line,” Romney told reporters here. “My view is that those people who have waited in line patiently to come to this country legally should be ahead in line, and those who’ve come here illegally should not be given a special deal or a special accelerated right to become a permanent resident or citizen.”

Asked whether he considered Gingrich’s immigration position to be “amnesty,” Romney said he did.

“It certainly was for the people he was referring to,” Romney said. “He didn’t go on and describe how about someone who’s been here 20 years? How about 12 years? How about 10? Five? Three? How many children do you have to have to apply this principle? He didn’t describe that.”

Meanwhile, Gingrich took to Twitter to refer supporters to what he called a “10-point plan to enforce the law, secure the border and reform our broke immigration system.”

Gingrich also took a swipe at Romney, by sending a tweet to the former Massachusetts governor: “Here’s a trip down memory lane.” Gingrich’s tweet included a clip from a 2007 “Meet the Press” interview in which Romney said: “Those people who had come here illegally and are in this country, the 12 million or so that are here illegally, should be able to sign up for permanent residency or citizenship.”

But Gingrich edited out of his clip the latter half of Romney’s quote, in which Romney said: “They should not be given a special pathway, a special guarantee that all of them get to stay here for the rest of their lives merely by virtue of having come here illegally.”

Meanwhile, the Obama campaign, which never misses an opportunity to portray Romney as inconsistent, held a conference call to denounce his immigration stance following Tuesday’s debate. That put the Democratic officials in the odd position of virtually endorsing Gingrich on the issue.

Rep. Silvestre Reyes (D-Texas) noted that in an earlier era, Romney had supported legislation proposed by Sens. Edward Kennedy (D-Mass.) and John McCain (R-Ariz.) to help expand legal immigration. Now, Reyes said he was “profoundly saddened and disappointed” by Romney’s criticism of Gingrich.

“I think Romney gives flip floppers a bad rap,” Reyes said. “I don’t think we really know what his position may or may not be.”

Reyes compared Romney’s desire to deport immigrants to attacks on his Mormon faith, which he said had been criticized as “cult-like.”

“What’s disturbing is, he’s the one who’s had to endure the attacks on his religion, and for him to now take this kind of position -- it’s in­cred­ibly perplexing,” Reyes said on the call.

“You would think he would…take a more tolerant view of what Gingrich was trying to promote.”

Although Romney fielded questions about immigration policy during his press conference, he was not pressed to discuss the subject during a carefully choreographed visit to Nationwide Insurance’s offices here. Addressing about 300 employees in the company’s second-floor cafeteria, and later fielding questions from a handful of them, Romney kept his focus on President Obama and the economy.

Romney appeared here with his newest big-name endorser, Sen. John Thune (S.D.), who considered a presidential bid of his own but decided against running earlier this year. Romney joked that a year and a half ago, when he was plotting a 2012 presidential campaign with his advisers, they discussed who might be his toughest opponent.

“The number one answer came about some senator from South Dakota that I had never met,” Romney said. “And he’s here with me today. I’m so lucky he didn’t run.”

The two enjoyed an easy banter. As he walked to the podium to begin the event, Romney gestured toward Thune and said: “You’re wondering who this tall, good-looking guy is over here. It’s actually Tom Brady of the New England Patriots.” Thune said he was pleased to campaign with Romney in “my neighbor state.”

One Iowan stood up and acknowledged the difficulty of defeating a sitting president and asked Romney: “What magic tricks do you have in your hat?”

“If I had a secret plan, I wouldn’t tell you,” Romney said, laughing. “But the secret is, my plan’s out in the open, and that is talk about the economy day in and day out… The reason I’m the guy to take that Republican banner and take that message is because I understand the economy. It’s in my wheelhouse. This is not something I need to get briefed on by [Obama Treasury secretary] Timothy Geithner.”

More on PostPolitics

Anne Kornblut contributed to this story