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"This week, here in Washington, D.C., we are celebrating Hispanic Heritage Month. But yet at the same time, we have this cloud hanging over us," said Cárdenas, "where we have someone who has made it to be the nominee to one of the two largest political parties, and yet all he has to say about Latinos, Hispanos, are negative things."

Lujan Grisham said Hispanic entrepreneurial culture has been the backbone of New Mexico's economy.

"Building when it is really tough is an indication about what a community can achieve despite almost insurmountable odds," she said.

Guatemalan-born Torres referenced the Hispanic electorate's large numbers but relatively small voter participation rates.

"To the Latinos out there, too often, we have allowed people, like Donald Trump, to label us. Stop. Let’s show Donald Trump that this sleeping giant that everyone talks about is awake, and that he is responsible for it," Torres said.

Trump's campaign has made immigration and Latino issues central to the election. At his announcement in June of last year, he called Mexican immigrants "rapists" who "bring crime," and promised to build a wall on the border with Mexico.

But Latino voters are expected to play a key role in several swing states, raising their relevance in the presidential race.

Trump has at times reached out to Latinos — most notoriously with his Cinco de Mayo taco bowl tweet — and rephrased his rhetoric on immigration, but has remained adamant about building a border wall.

"His insults are direct and obvious," said Becerra. "His attempts to compensate are just as insulting. He can't hide who he is."