"There was so much corruption with Congress, scam after scam," said Ravinder, a 19-year-old business administration student at a Modi rally in Uttar Pradesh on Sunday.
"Now we see hope. There is someone talking about development, and he seems sincere."
Polls show the BJP well short of a majority of the 543 lower house seats at stake, but widening its lead over Congress, which has ruled India for more than two-thirds of the 67 years since independence, but which may now face its worst electoral defeat.
A multi-headed group of regional parties is also eyeing power, reflecting the growing clout of state-based leaders.
A "third-front" government made up of such diverse groups could prove unwieldy when it comes to running Asia's third-largest economy, whose growth has faltered due to the slow pace of reform on the Congress party's watch.
(Read more: Is India going back to bullion?)
Leading the Congress party's campaign is Rahul Gandhi, scion of a dynasty that has given India three prime ministers and its most powerful contemporary politician, his mother, Sonia Gandhi.
But after two consecutive Congress-led governments headed by Prime Minister Manmohan Singh, India seems unlikely to make another Gandhi prime minister.
Economic growth is set to stay below five percent for the second year running, which would be the worst performance since the 1980s for a country that a few years ago was confident of matching China's run of double-digit expansion.
Modi has the backing of big business, which wants him to replicate his Gujarat state model of good roads, uninterrupted electricity and less red tape. Last week, he promised simpler laws and a trade-centred foreign policy, if elected.
As the election approaches, overseas investors have extended a buying streak of Indian shares, with purchases totalling $800 million in a run of 13 sessions until Tuesday.
(Read more: What India needs to do to stamp out poverty)
But businesses have put investment plans on hold, worsening a slowdown that could, however, be reversed after the polls.
"Irrespective of who wins, pent-up demand is set to be released after the elections are over," HSBC said in a research note. "Companies that have shelved expansion plans will at some point start investing and hiring."