The unattached prime minister is also seen as free of grasping family ties, and thus less corruptible. His three-year-old administration is untouched by scandal, a rare achievement. Many voters thus accept Mr. Modi’s argument that corrupt elites had been failing since independence in 1947, and his clean administration deserves more than three years to deliver on “vikas,” development.

My travels took me through Varanasi, a Hindu holy city that is the prime minister’s home constituency in Parliament. Residents blame state authorities for the squalor here, not Mr. Modi. On my way out of the city, a man told me I was about to witness “the many good things the state government has done for our roads and bridges,” in a tone so deadpan I couldn’t be sure if he was being sarcastic.

But the drive eastward quickly led into barren lands that evoke the “Mad Max” movies, as if someone had superimposed gas engines and mobile phones onto medieval villages. At the skeletal beginnings of a suspension bridge over the Ganges River, locals told me the bridge was incomplete 13 years after construction because each successive state administration halted work to turn the project over to its favorite contractors. Diverted toward a rickety pontoon bridge, I hit a mile of stopped vehicles, all halted by a car that had slipped off the steel slats. Later, fitness watches in our van started announcing “10,000 steps,” “15,000 steps” — apparently counting bumps in the road.

The development hurdles facing India are this basic, and many locals believe Mr. Modi is the answer. Manmohan Singh was seen as a tool of the Gandhis and was often overshadowed by a cabinet of powerful rivals, but Mr. Modi is the opposite — increasingly unchallenged and respected for it.

The World Values Survey found that between the mid-1990s and the early part of this decade, 25 of 30 countries that responded to the survey in both time periods saw an increase in the number of people who agree that having “a strong leader who does not have to bother with Parliament and elections” would be good for their country. In India, support for this proposition spiked to 70 percent from 44 percent, the highest level after Ukraine. India also ranked near the bottom in popular support for private enterprise, alongside former Communist bloc nations like Russia and Ukraine.

Mr. Modi’s makeover as a strong-arm champion of the poor is thus tapping into India’s fundamentally socialist DNA. His most striking use of state authority came on the evening of Nov. 8, when he announced that India would begin withdrawing large currency bills — 86 percent of the currency in circulation — starting at midnight.

Advertised as a way to force wealthy tax dodgers to turn in their “black money,” and catch them unawares, the scheme also threw the lives of poor savers into chaos. Yet Mr. Modi has managed to portray himself as a can-do leader and critics of the currency cleansing as elitist outsiders. “On one hand are those who talk of what people at Harvard say, and on the other is a poor man’s son who through his hard work is trying to improve the economy,” he said at the Deoria rally.