SATARA, India  Sunita Laxman Jadhav is a door-to-door saleswoman who sells waiting. She sweeps along muddy village lanes in her nurse’s white sari, calling on newly married couples with an unblushing proposition: Wait two years before getting pregnant, and the government will thank you.

It also will pay you.

“I want to tell you about our honeymoon package,” began Ms. Jadhav, an auxiliary nurse, during a recent house call on a new bride in this farming region in the state of Maharashtra. Ms. Jadhav explained that the district government would pay 5,000 rupees, or about $106, if the couple waited to have children. Waiting, she promised, would allow them time to finish their schooling or to save money.

Waiting also would allow India more time to curb a rapidly growing population that threatens to turn its demography from a prized asset into a crippling burden. With almost 1.2 billion people, India is disproportionately young; roughly half the population is younger than 25. This “demographic dividend” is one reason some economists predict that India could surpass China in economic growth rates within five years. India will have a young, vast work force while a rapidly aging China will face the burden of supporting an older population.

But if youth is India’s advantage, the sheer size of its population poses looming pressures on resources and presents an enormous challenge for an already inefficient government to expand schooling and other services. In coming decades, India is projected to surpass China as the world’s most populous nation, and the critical uncertainty is just how populous it will be. Estimates range from 1.5 billion to 1.9 billion people, and Indian leaders recognize that that must be avoided.