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Democrats see a rich source of votes among Hispanics, whose growing numbers could provide a bonanza for the party that reaches them first. But Hispanic voters haven’t completely aligned themselves with Democrats, and neither party has done enough to reach them, said Marcelo Gaete of Mi Familia Vota, which focuses on registering Hispanic voters in Colorado and Arizona.

“Whenever I hear about the ‘sleeping giant,’ I want to vomit because it implies there’s something wrong with Latino voters,” Mr. Gaete said. “Latino voters behave just like everyone else does when they’re ignored.”

He recommended focusing on naturalized Hispanic citizens, whom he called “citizens by choice,” noting that they vote in higher numbers than U.S.-born voters. Naturalized citizens represent 45 percent of registered Hispanic voters but 51 percent of those who cast ballots, he said.

The Democratic analysts agreed that tax increases are a tough sell with Western voters, particularly in lean budgetary times, on everything except education. Still, they said, Democrats need to counter GOP arguments depicting government as a negative.

“We don’t have the right language when it comes to these debates. We’re Democrats, or progressives, if you will,” said Andrew Myers, president of Myers Research and Strategic Services. “We can get away with it on education, but in the long term it’s a losing strategy.”

He added that “connecting with people is the challenge for both parties.”

“There’s a tension about public services more generally,” said Mr. Myers. “The conundrum is the states [are] having budget shortfalls when public services are most needed.”