María Carvajal, 41, who cleans houses in the state capital, Toluca, said that the PRI, which governed Mexico for seven decades before being dumped by voters in 2000 and returning to power under Mr. Peña Nieto in 2012, often hands out money or food packages at election time. The State of Mexico is Mr. Peña Nieto’s home state and a PRI bastion.

“I don’t think it is fair to just try to buy people off like that,” she said, describing how she received her television coupon. “It is the same with the TVs, and it has always been this way.”

There are big issues at stake in this election, which will choose all 500 members of Mexico’s lower house of Congress and almost a third of the country’s governors, as well as mayors and legislatures in more than half of the states.

Mr. Peña Nieto needs a working majority in Congress to support a budget overhaul in response to falling oil revenues and to restart his stalled security proposals. A majority would also give his party control over writing the fine print of a new anticorruption system it supported reluctantly.

Polls show that more than half of Mexicans disapprove of the president’s job performance. His standing has been battered by a scandal over his wife’s purchase of a mansion from a government contractor and his government’s handling of an investigation into the disappearance of 43 students.

Amid continued drug violence and meager economic growth, about two-thirds of Mexicans believe that the country is on the wrong track, according to Francisco Abundis, director of the polling firm Parametría.

Five candidates have been killed, including one shot dead on Tuesday. Teachers opposed to a broad education overhaul promise to boycott the election in the states of Guerrero and Oaxaca. Since Monday, demonstrators have stormed the National Electoral Institute’s offices in both states, destroying equipment and burning ballots.