LAS VEGAS—After two days of meetings at the Republican Governors Association conference, New Mexico Gov. Susana Martinez on Thursday said she heard a lot about the party's need to reach new constituencies—particularly women and ethnic minorities—but few specifics about how.

As a Republican governor of Mexican descent who won all but four counties in a Democratic state, Martinez has ideas for how the party can reach voters who traditionally support Democrats. But it's going to take some work, she noted, and a touch of humility, from her colleagues.

"Republicans need to stop making assumptions, and they need to start talking to younger people, people of color, and ask them—not talk to them—ask them, 'What is it that we can do better? How do we earn your vote? How do we earn the ability for you to see that we can be the party that will make your life better and that of your children?'" Martinez said in an interview after the conference here. "But we can't be the ones that come and tell them how things are going to be and how we have all the solutions."

President Barack Obama in 2012 expanded his lead among Hispanic, black, Asian and women voters, according to exit polling, leaving many Republicans wondering what they need to do to adapt to the nation's rapidly shifting demographics.

The topic has dominated much of the party's postelection soul-searching. Some have placed part of the blame on Mitt Romney for writing off 47 percent of the electorate as inevitable Obama voters at a closed-door fundraiser last spring—his comment, said Martinez, was "ridiculous"—and then, postelection, saying he lost to Obama in part because the president promised "gifts" to minority voters in return for their support.

"That unfortunately is what sets us back as a party, our comments that are not thought through carefully," said Martinez, whose name was discussed in the national media as a possible running mate for Romney but who was never vetted for the job.

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In order to make inroads with minority voters—particularly Hispanics—Martinez urged Republicans to pursue immigration reform and to begin grass-roots outreach now instead of waiting until an election year to seek votes.

"We need to embrace them not just at election time. ... We should not visit them when we need their vote and then walk away," Martinez said. "And then four years go by and we go visit them again. We have to make them part of the solution, and the way you do that is by listening to them and then making that part of 'How do we do this together to make our lives all better?'

"And then once you've done it," Martinez added, "you tell them we did it together."