“He is good-looking,” said María Alonzo Barragán, 52, as the candidate moved through the crowd. “But he is also honest, responsible and hard-working.”

Promising a Difference

Ms. Vázquez Mota also started her campaign early Friday, with a smaller rally at her party headquarters in Mexico City, where she immediately argued that the P.R.I.’s years of control “are still holding us back.” Her campaign slogan — “Josefina Diferente, Presidenta 2012” — also signaled to voters, perhaps with a wink, that she was not like those other guys in her party, Mr. Calderón and his predecessor, Vicente Fox.

She is not just a woman, her campaign suggests. She is a woman who understands struggle, having grown up in a shabby one-story home that she visited for breakfast on Friday morning. And, her first day on the trail aimed to show she is a woman ready to listen.

“What would you like to see different?” she asked again and again on Friday, in a classroom of second graders at the school she attended as a child. “If we work hard, all dreams are possible.”

Speaking to the adults, mostly women, she also made clear that while Mr. Peña Nieto was most comfortable speaking in platitudes, she preferred to address issues that hit closer to home. Her promises were those that she, as a working mother of three, knew they wanted to hear: a full school day with afternoon activities so that children could play sports, learn an instrument, read more books and do their homework; a little more help so that overtaxed families could “share time together.”

That message sounded fresh and appealing to some.

“If you know how to run a house, why can’t you run a country?” said Laura Rodríguez, 35, a single mother of three, who said she had been persuaded on the spot to vote for Ms. Vázquez Mota. “Men are always first; where is the space for women, who are always left behind?”

And yet, if Ms. Vázquez Mota, 51, can win only by proving how different she really is, are after-school programs enough? Luis de la Calle, an economist and a former under secretary of international trade, said Ms. Vázquez Mota and Mr. López Obrador could overcome Mr. Peña Nieto’s strong lead only by making bold proposals. “The average Mexican is a lot more modern than our politicians,” he said. “The average Mexican is willing to hear more about Mexican taboos like reforming the energy sector or really changing the tax system.”