Then there is the problem of Democratic infrastructure: there hasn’t been one for years. In 1995, Ron Kirk forged a coalition of Hispanics and African-Americans to become the first black mayor of Dallas, but he could not do the same statewide; he lost a Senate race to John Cornyn in 2002.

That same year, the millionaire oilman Tony Sanchez, a Democrat running for governor, had money, a Mexican heritage and an ability to appeal to Mexican-American voters. For it, he still lost 35 percent of the Hispanic vote to Mr. Perry, who claimed the governor’s mansion.

But the biggest problem is voter participation. Only about half of eligible Hispanic voters show up nationwide; this edged up slightly in 2012 to 53 percent. In Texas, just 4.1 million Hispanics are registered to vote, and only about half of them make it to the voting booth.

Why? There are a variety of explanations, including cultural ones. It’s pretty easy to feel disenfranchised by a political system that talks about you as an “immigrant” or, worse, an “alien.”

The Democrats have a few things working for them. The national Republican Party and its immigrant-bashing tendencies is one, of course. And it has hitched its outreach wagon to two senators — Marco Rubio of Florida and Ted Cruz of Texas — who are Cuban-American, a difference that may seem minor to non-Hispanics but that significantly diminishes their appeal to Texas’ Latinos, who are primarily of Mexican heritage. (Indeed, the Canadian-born Mr. Cruz actually got fewer Hispanic votes last year than Mr. Cornyn did in 2008.)

It may be that the demographic wave makes all this beside the point, and that increasing turnout among Hispanics just a little might make a big difference.

But that requires ground troops, voter education and turnout efforts over a multicycle campaign. It also requires that Democrats stop assuming they’re going to lose. “If we start treating this as a purple state,” said Matt Glazer of the activist group Progress Texas, “we would be one that much sooner.”