The head of Mitt Romney's campaign to attract Latino voters during the presidential election has warned fellow Republicans that unless they embrace immigration reform they are in danger of destroying the party's reputation as the guardian of economic freedom and prosperity.

Carlos Gutierrez, former commerce secretary under George Bush and the man who spearheaded of Romney's outreach to the Hispanic community, has called on the Republican party to drop its perceived hostility towards the 11 million undocumented immigrants in the US or risk alienating the increasingly powerful Latino vote. He has set up a Super Pac called Republicans for Immigration Reform to instill new thinking within the conservative movement.

"What we want to do with the Super Pac is to provide some intellectual cover to Republicans so that they can move forwards without being politically hindered. If we are to remain the party of entrepreneurs and economic freedom and American prosperity, we have to also be the party of immigration," Gutierrez told the Guardian.

Gutierrez is one of a growing number of influential Republicans who have spoken out since Romney's defeat on 6 November in favour of reform. Key party figures, including the speaker of the House of Representatives, John Boehner, former presidential candidate John McCain and the South Carolina senator Lindsey Graham, have signalled that they are ready for a radical rethink.

The sharp shift in political tone on the right of American politics is a reflection of simple electoral mathematics. Romney lost in no small part because he succeeded in driving Latino voters into the Democratic camp with his talk about the "self-deportation" of undocumented immigrants during the primary contest for the Republican nomination.

Analysis of exit polls by the Pew Research Center shows that Hispanics flocked to Barack Obama by 71% to Romney's 27% – a demographic landslide only surpassed in modern times by Bill Clinton in 1996.

An overwhelming 77% of Hispanic voters – all of whom are by definition US citizens – said that they wanted undocumented immigrants to be given a chance to become legal residents.

Pew's work underlines the inexorable rise of the Latino vote, which accounted for 10% of all voters in this year's presidential election, up from 9% in 2008 and 8% in 2004. The growing power of the Hispanic electorate was particularly pronounced in three vital battleground states – Colorado, Florida and Nevada – all of which Obama won convincingly.

Gutierrez said that Romney had fallen foul of the Republican primary trap, where presidential candidates are forced to adopt far-right positions in order to appeal to the extremist rump of the party and win the nomination. Romney tried to find his way back to a more moderate stance on immigration in the general election against Obama, but by then it was too late.

"I did a lot of campaigning in Florida and Virginia, and I saw that the Republicans' far-right positions in the primaries had scared Hispanic voters. Things like 'self-deportation' that weren't ever really defined but sounded very scary," Gutierrez said.

The sudden outpouring of self-criticism on the part of Republican leaders about the party's aggressive immigration position raises the prospect of a bi-partisan push on reform for the first time since Bush failed to pull off a deal in 2006. Obama has promised to make a comprehensive reform package a priority of his second term, saying that he expects Congress to propose a reform bill early next year.

"There's clearly a consensus among Republican leaders that we have to change the tone with which we talk about immigration policy and Hispanics in general," said Whit Ayres, a Republican pollster who has tracked the rise of the Latino vote for many years. "There's a recognition that some adjustment needs to be made in the party's policies, though there's no consensus yet as to what the new approach should be."

There are already signs of the conservative movement splitting into two main camps. Marco Rubio, the ebullient Florida senator who is already positioning himself for a run on the White House in 2016 , has been pressing for limited immigration reform that would be confined to so-called "Dreamers" – young Latinos brought to the US illegally as infants.

Other senior Republicans, including Gutierrez, want to see more comprehensive reform that would address the conundrum of all 11 million undocumented immigrants. "We believe that most Republicans want to solve this problem. They recognise that our laws are 50 years old and no longer work, and that this issue is all about finding new human capital for the 21st century."

Republicans for Immigration Reform, which Gutierrez has formed together with Charlie Spies, co-founder of Romney's largest Super Pac during the election, Restore Our Future, argues that all undocumented immigrants should be given a path towards legality. They would be encouraged to register with the US government after which they would be granted an authorisation card that would allow them to work.

Gutierrez stresses that under the new Super Pac's reform proposals, there would be no automatic route to citizenship. Legalised immigrants would have to apply for a Green Card just like everybody else.