LOS ANGELES -- During a decade in the U.S., Mexican immigrant Linex Rivera gave birth to three daughters, whose American citizenship offered her hope of staying in the land of opportunity. But with job prospects drying up for her husband, Ms. Rivera last week joined a phalanx of compatriots at the Mexican consulate in Los Angeles inquiring about obtaining Mexican citizenship for their children.

"We are thinking of returning to Mexico and want our daughters to have all the rights of Mexican nationals," says Ms. Rivera, whose...