Prominent Republicans are launching a new super PAC they hope will help begin repairing the political damage left by years of anti-illegal-immigrant rhetoric that has dominated GOP primaries and alienated crucial Hispanic voters.

The organization, to be called Republicans for Immigration Reform, aims to undermine what organizers call the “extremists” who have pushed party nominees to stake out far-right positions such as opposing a pathway to legalization for millions of illegal workers, students and children.

Even before it raises money and establishes target races for 2014, the group’s organizers told The Washington Post, it will help smooth the way for wavering Republican lawmakers to vote next year for an immigration overhaul. Such a measure suddenly gained momentum last week after GOP leaders watched President Obama’s dominance among Hispanic voters help carry him to an electoral college landslide.

Spearheading the group is Carlos Gutierrez, the Cuban American commerce secretary under President George W. Bush. He is joined by Washington lawyer Charlie Spies, co-founder of the pro-Mitt Romney super PAC Restore Our Future, which, illustrating the very trend that the new PAC aims to thwart, aired some tough ads during this year’s primaries accusing Romney’s rivals of supporting “amnesty” and being “too liberal on immigration.”

“There’s currently only energy on the anti-immigration reform side, and we want to be able to provide some cover for Republicans that vote in support of an immigration reform approach,” Spies said.

Spies and Gutierrez declined to cite a fundraising goal, but both enjoy close ties to corporate America, which generally favors looser immigration laws. A super PAC can accept unlimited donations. Spies’s pro-Romney group raised $142 million for the 2012 campaign, according to the Center for Responsive Politics.

“This is not small ball,” Gutierrez said. “We’re serious, and we are going to push the debates on immigration reform to a place where I believe the Republican Party should be in the 21st century.”

Gutierrez, who was a top Romney adviser, gained attention over the weekend when he told Univision anchor Jorge Ramos that the Republican nominee lost to Obama because the GOP “frightened the American people” during its primaries.

He told The Post that he regretted some of Romney’s remarks on immigration during the campaign. Romney used the issue to fend off challenges from Texas Gov. Rick Perry and former House speaker Newt Gingrich, accusing both men of being soft on illegal immigration. At one point, Romney endorsed a policy of “self-deportation” for immigrants in the country illegally, adopting the language of some of the country’s most ardent critics of illegal immigration.

“Mitt Romney’s comments were a symptom of the disease of the Republican Party, and the extreme far-right wing that is way out of the mainstream of Americans’ views is the cause,” Gutierrez said. “Governor Romney was forced to say things that got him into a lot of trouble. And the irony of it is that had he not said those things, he wouldn’t have been the nominee.”

The result was Romney winning just 27 percent of the Hispanic vote — less than John McCain in 2008 and far less than Bush’s 40 percent support level for his 2004 reelection.

Bush and his senior strategist Karl Rove tried to push their party to the left on immigration, arguing that Hispanics are a fast-growing voter segment in key swing states. But conservatives rebelled when Bush tried in his second term to create a path to citizenship, and GOP orthodoxy ever since has required candidates to take a hard line against such policies.

Spies said the new PAC will most likely favor whatever immigration plans are backed by House Speaker John A. Boehner (R-Ohio) and Sen. Marco Rubio (R-Fla.), a Cuban American and possible 2016 presidential candidate who is expected to be a central GOP player on the issue, although both lawmakers have staked out conservative stances in the past.

The challenge ahead for the GOP was evident last week when Boehner stepped out to endorse a “comprehensive” approach to the immigration issue — only to be denounced by some House conservatives for sounding as though he was preparing to back an “amnesty” plan. Boehner later backtracked a bit but still said he was committed to acting.

Gutierrez and Spies are not alone in speaking out for a new GOP approach to immigration.

Former Florida governor Jeb Bush, another possible 2016 presidential candidate, has long derided critics of new immigration laws and is co-writing a book on the issue. His wife, Columba, is Mexican American.

Their eldest son, George P. Bush, who has worked to recruit Hispanic GOP candidates in Texas, recently filed papers there to run for statewide office, although it’s not clear which one. A fundraising appeal from his father suggested that he was interested in running for Texas land commissioner.