PHOENIX — In the humble building that houses her lofty mission, Alexis Tamaron senses the moment and understands the opportunity.

She also has realistically sized up the hurdle.

Tamaron, deputy state director for the Howard Dean campaign in Arizona, believes her guy is a goner if he does not win here Tuesday. And she believes the ex-governor of Vermont needs a boost from the state's large Hispanic community.

So she laughs when reminded that the most famous Hispanic name in Vermont is Ben and Jerry's Cherry Garcia ice cream.

But Tamaron is bolstered by the fact that all the Democratic contenders are from far away places, none with much of an Hispanic feel.

On Tuesday, with that storyline, Hispanics could have an unprecedented impact on the selection of an American president. In New Mexico, the nation's most Hispanic state, there will be caucuses. In Arizona, voters go to the polls.

The task for Tamaron, who sees Hispanics as a "very big key part" of Dean's chances here, is marketing a Vermonter in the Southwest.

Feeling the pressure?

"A bit," she said with a nervous laugh. "Just a bit."

On Saturday in Tucson, her candidate, moments after waving a piata handed to him by a supporter, declared the Hispanic vote "very important."

"We've got some Spanish-language television," he said, failing to note that his campaign is running no ads in Arizona.

In various ways, the Democratic contenders are paying attention or lip service to the Hispanic vote up for grabs Tuesday. Some do it with Spanish-language ads. For some, it's an arms race waged with Hispanic endorsers.

For all, there is acknowledgement that someday — maybe Tuesday — the Hispanic vote will be pivotal if it ever turns out in numbers reflecting its status as the nation's fastest growing community.

Dean, John Kerry, Wesley Clark, Joe Lieberman and Dennis Kucinich are scheduled here Monday at a League of United Latin American Citizens forum.

At the University of New Mexico, political scientist Lonna Atkeson said thanks to the confluence of calendar and circumstance, Tuesday offers a major opportunity for Hispanics.

"They are certainly playing a bigger role than they've ever played before," she said.

Tuesday's Southwest contests play out amid an electorate far more like America's demographic future than are Iowa (3 percent Hispanic population) and New Hampshire (under 2 percent Hispanic).

And the contests will be played in states that look nothing like the candidates' home states.

Arizona's population is 25 percent Hispanic. New Mexico's is 42 percent. Lieberman's Connecticut? Nine percent Hispanic. Kerry's Massachusetts? Seven percent. Clark's Arkansas? Three percent. John Edwards' North Carolina? Five percent. Dean's Vermont? Just under 1 percent.

New Mexico State Democratic Chair Joni Gutierrez laughed when asked if any of the contenders have a natural link to Hispanics. "I guess some are built more like Hispanics than others," she joked. "A lot of people think Howard Dean looks like the Albuquerque mayor, Martin Chavez."

"That same border-state look," Gutierrez said. "Vermont is a border state."

So, some believe, the connection to Arizona and New Mexico Hispanics can be best made through surrogates. Kerry has former San Antonio Mayor Henry Cisneros, who will campaign here again Sunday.

"Here's a state, Arizona, that has talked about wanting more voice," Cisneros said as he prepared for the trip. "And here are Latinos who have been saying they want more of a voice. Now they can have a disproportionate say."

Sen. Edward Kennedy, D-Mass., made a round of Friday stops on Kerry's behalf in Phoenix. At Cesar Chavez High School, he reminded the locals about his family's ties to Chavez.

"Arizona, New Mexico are not New Hampshire and not Iowa," he said, playing up the importance of the Tuesday contests in heavily Hispanic states that could be crucial in November as the Democrats focus on the area to make up for expected losses in the South.

The potential southwestern strategy could include selection of New Mexico Gov. Bill Richardson, a Hispanic, as the Democrats' vice presidential candidate.

Richardson has not endorsed a candidate, but at a Saturday event for Edwards in Albuquerque, complete with mariachis, the governor noted that Edwards has visited New Mexico more than any other candidate.

Hispanic Rep. Ed Pastor, D-Ariz., signed on as a Kerry national co-chair (with Kennedy, Cisneros and California Sen. Dianne Feinstein) after the New Hampshire primary.

New Mexico's other Hispanic congressman, Rep. Raul Grijalva, is a Dean backer.

While most of the candidates miss no opportunity to acknowledge Hispanics, Clark talked to a Phoenix crowd for 33 minutes last week without once mentioning them.

Afterward, as he shook hands, a question about the Hispanic vote drew only an abrupt "We are going to work for it."

Earlier that day, in Albuquerque, Clark introduced himself in Spanish before asking "Continuamos en ingles, por favor?" and continuing in English.

Mark Riddle, Clark's Arizona state director, said there is no effort — save for translating the message — targeting Hispanics.

"The Hispanic community is so large here in Arizona it actually just becomes part of your comprehensive plan," he said. "It's no longer a small interest group you cater to."

Kerry's Arizona director, Mario Diaz, said he is targeting Hispanics, veterans and senior citizens.

But Diaz is not putting much effort at bringing new Hispanic voters to the polls, opting instead to work on Hispanics who have been voting.

"It's not about quantity, it's about the type of voter we get to the polls," he said.

On an ad airing in Arizona and New Mexico, Kerry speaks Spanish, but only to add the required disclaimer: "I'm John Kerry and I approved this message because I want to return hope to this country."

While some observers say Hispanics could be the difference-makers, Paul Hegarty, executive director of the Arizona Democratic Party, cautions against overplaying it.

"Hispanics will not be the one determining force," he said. "If you win the Hispanic community it doesn't mean that you are going to win the state. But you can't factor in not involving Hispanics in your campaign."

As in many states, Hispanic turnout in Arizona has been disappointing for many years, hovering around 35 percent in recent elections. At Dean headquarters, Tamaron is among those who have been trying to figure out how to do something about that.

She sees a cultural barrier, rooted in Mexico's different notion of democracy.

"It's a big education problem," she said. "Because even if you are second or third generation you have historical knowledge from your parents who don't necessarily believe in the system, that it doesn't really matter, that (politicians) are just going to do what they want anyway."

For Tamaron, Tuesday is a big day for her candidate and her people. She is trying not to think about what a low Hispanic turnout would mean for both.

"I think I would be incredibly disappointed because it's an opportunity for the Latino community to flex some muscle on a national level," she said.

It's a message Tamaron says Dean's door-to-door force is shopping on a daily basis.

"You say to them, 'This is it, it's coming down to the wire and you have to come out to make a difference.