The pipes are laid, the taps installed and the village tank is under construction — all promising signs that, come spring, Girja Ahriwar will get water at her doorstep and finally shed a lifelong burden.

“I go out and put the jerrycans in the queue at around 5 a.m. and wait there with the children,” Ms. Ahriwar, a mother of three who lives in the central Indian state of Madhya Pradesh, said about her routine of fetching from the village hand pump. “Sometimes it could take five or six hours. I have to stay there because if I leave, someone else moves ahead.”

India, one of the world’s most water-stressed countries, is halfway through an ambitious drive to provide clean tap water by 2024 to all the roughly 192 million households across its 600,000 villages. About 18,000 government engineers are overseeing the $50 billion undertaking, which includes hundreds of thousands of contractors and laborers who are laying more than 2.5 million miles of pipe.

The project has a powerful champion in Prime Minister Narendra Modi, who has slashed through India’s notorious red tape and pushed aside thorny political divisions to see it through. His success thus far helps explain his dominance over the country’s political landscape.

Mr. Modi has remained popular despite a weak economy and a bungled initial response to the coronavirus that left hundreds of thousands dead. He has increasingly relied on communal politics, continuing to consolidate a Hindu nationalist base he has worked for decades to rally.

But the mission to deliver water to every household combines two of Mr. Modi’s political strengths: his grasp of the day-to-day problems of hundreds of millions of India’s poor and his penchant for ambitious solutions. Mr. Modi, who grew up in a poor village, has spoken emotionally about his own mother’s hardship in fetching water.

About one-sixth of India’s households had a clean water tap when the program, called Jal Jeevan Mission, began in 2019. Now, almost half have one.

“You rarely have this drive from the government, the head of state, and it is well funded. Behind the concept, there is budget,” said Nicolas Osbert, who leads the UNICEF water and sanitation unit in India. “All social sectors were impacted by Covid. Not this one. This one was preserved.”

The country’s water problem speaks to the mismatch between its global economic ambitions and the dire conditions of much of its 1.4 billion population, two-thirds of whom still live in rural areas. Nearly 40 million Indians are affected by waterborne diseases every year, leading to about $600 million annually in medical costs and labor loss. About 100,000 children under 5 years old die of diarrhea every year. The growth of millions more is stunted.

“The paucity of water should not become a limiting factor in our quest for socioeconomic development, the quest for high economic growth,” said Bharat Lal, the top official Mr. Modi has named to lead the mission.

From his office in New Delhi, Mr. Lal checks the progress on a detailed computerized dashboard. About 100,000 connections are added every day, according to official figures, and Mr. Lal’s phone pings constantly with videos and photos showing successes.

The mission judges progress by the satisfaction of village councils to avoid slowdowns from India’s layered bureaucracy. Districts and states are teamed up with technical universities for comment on best practices. Local organizations handhold village councils as they take on the role of public utility managers.

The village bodies are expected to collect a small monthly fee — about $1 per household — to have funds for maintenance and to encourage a culture of participation and ownership.