“We were never wealthy, for sure,” Mr. Castro said. “My grandmother had a Social Security check that she would get on a monthly basis, and we would look forward to that when she got it, Joaquin and I, because we would run off to the store to go buy soda or Cheetos or whatever. The income levels changed, but the one constant was that both my mother and my grandmother were always very, very supportive, and they made both of us feel like we could do anything.”

A lawyer and former city councilman, Mr. Castro represents a new generation of Hispanic-American leaders in Texas from both parties who perhaps identify more with the second half of that descriptor than with the first, and who have broad appeal among minority and white voters. Mr. Castro’s chief of staff, Robbie Greenblum, speaks fluent Spanish, but the mayor of this majority-Hispanic city does not, though he has been working to improve.

“He positions himself as a politician who is Latino, rather than a Latino politician,” said Walter Clark Wilson, an assistant professor of political science at the University of Texas at San Antonio. “The nuance is that he wants to be seen as someone who can represent everybody.”

Last year, Mr. Castro won a second two-year term with nearly 82 percent of the vote.

His critics, particularly those who believe he is more hype than substance, are easier to find outside San Antonio than in it. “It seems to me that he has a very light record of actual accomplishment,” said Matt Mackowiak, a Republican political consultant in Austin. “In a way, there’s a real parallel to Obama, because this is an aspirational candidate, not a candidate who runs on a record of accomplishment. He may not have any enemies, but that’s probably because he hasn’t done anything.”

In many ways, Mr. Castro’s moment in the national spotlight will also belong to the city he has led, which will be reintroduced to many who know it merely as the home of the Alamo.

San Antonio has become a kind of Berkeley of the Southwest, a progressive, economically vibrant and Democratic-leaning city of 1.3 million in Republican-dominated Texas. A few blocks from City Hall, mariachi singers with acoustic guitars serenade diners at Mi Tierra with old Mexican ballads, while outside sits something new: a row of bicycles ready for renting, part of the city’s popular bike-sharing program. Last year, the Milken Institute, an economic policy institute in Santa Monica, Calif., named San Antonio the best-performing city in the country, based on its ability to create and sustain jobs.

The speculation lately about Mr. Castro’s future has reached fever pitch; there is talk of his running for governor, earning a place in Mr. Obama’s cabinet and even becoming the first Hispanic president. A Fox News Latino headline this summer read: “Julián Castro: Son of Chicana Activist, Harvard Law Grad, Future U.S. President?”