TORIBIO ORTEGA, who supposedly fired the first shot in the Mexican Revolution a century ago, would have been surprised if told that a descendant of his would one day run an American state. So would Adolfo Martinez, another Mexican revolutionary, who crossed the sparsely patrolled border into America in the 1920s (whether legally or not is unclear from census records). But today Susana Martinez of New Mexico, great-granddaughter of the former and granddaughter of the latter, does just that: she is America's first Latina governor.

Her Democratic predecessor, Bill Richardson, is of Mexican descent on his mother's side. And Brian Sandoval in Nevada is both Latino and Republican. But Ms Martinez is the only governor who is simultaneously Hispanic, female and Republican. As such, she seems well on the way to embodying the party's hoped-for future as a conservative movement that can appeal to, rather than repel, Latinos, America's fastest-growing main ethnic group.

This is why many Republican strategists are now studying her. New Mexico, which has the highest share (almost half) of Latinos of any state in the country, is, along with Colorado and Nevada, an important swing state for 2012. John McCain, the Republican candidate last time and a senator from Arizona, thinks that Latinos are up for grabs in these states and even in his own, if Republicans will just change their nativist tone.

This is old news to Ms Martinez. Sitting in Santa Fe's remarkably informal Roundhouse, as the state capitol is nicknamed in homage to old Navajo hogans, she describes her conversion to Republicanism as a Damascene moment. Like most Latinos, she and her husband, Chuck Franco, started out as Democrats “because our parents were”. Then, one day in the 1990s, she and Mr Franco had lunch with two local Republicans. “They just asked questions, never asked us to switch party,” recalls Ms Martinez. And yet, as they sat in the car after the lunch, Ms Martinez turned to her husband and said, “Chuck, we're Republicans. What do we do now?”

She is only now beginning to work out her answer. Last year, when she ran for governor, she focused less on philosophy and more on fatigue with Mr Richardson, a Democrat who was termed out of office but had a reputation for sleaze. (A probe by a grand jury, the latest of several, is investigating alleged campaign-finance problems dating to his run for president in 2008.)

So Ms Martinez, so far, has simply tried to represent clean government. Her most photogenic act was to sell the state jet, a Cessna Citation Bravo, which Mr Richardson, she implied, had used as “a personal air taxi”. She even fired his cooks.

But the biggest issue for Latinos nationwide has been the new virulence among Republicans towards illegal immigrants, after radical legislation last year in neighbouring (and much whiter) Arizona. Ms Martinez has said little about the Arizona law and what it means to her “as a woman and as a Latina”, says Christine Marie Sierra, a politics professor at the University of New Mexico. But she has had a lot to say about law and order.

Tough and wonkish

Ms Martinez has embarked on an effort to stop issuing driving licences to illegal aliens. Only New Mexico and Washington state currently do this. (Utah issues permits.) Proponents argue that this policy, which also dates from Mr Richardson, lets more drivers get insurance and helps police to collect information. But Ms Martinez says it has turned into a racket, in which foreigners (not just Mexicans) sneak into the state for licences, then exchange them in other states to become documented.

For an Anglo politician, this would be a minefield. Even for Ms Martinez, it has caused problems, as Latino groups have accused her of being a traitor to her race. The ambiguity about her immigrant grandfather does not help. But her stance has not hurt her with voters or with Latinos in general. With a legislature that still tilts Democratic, she may or may not prevail. But her main objective may be to leave the topic of immigration at that, in order to move on.

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To what? This is where that lunchtime conversion in the 1990s comes in. Ms Martinez has a wonkish side. The state's small budget is unusual in having turned into surplus. And she cares about education, a sore spot for the state. One of her few successes to date has been a new education policy, which grades schools from A to F. Ms Martinez will now fight for other reforms considered conservative, eventually including proper evaluations for teachers. And this, she says, is the way to grab Hispanics: “Latinos care about education, yes, so we need reform, not just money.”

And so, conservatively, she moves on, from the environment to lower, simpler taxes and the rest. When necessary, she also looks the part. She shot a mean pistol when renewing her gun licence (which Jay McCleskey, a consultant who has been called a New Mexican Karl Rove, made sure to capture on video). Her husband wears gigantic cowboy hats.

If she does not talk about being Latina, it is because she has no need to. And yet, she says, it is the reason why she would turn the party down if it asked her to become the vice-presidential nominee: “I'm often introduced as the first Latina governor. With that comes an enormous responsibility,” she says. “Those little girls watching me have to see me deliver my promises.” So she will finish her term, as Sarah Palin in Alaska did not. What happens after that remains to be seen.