He has two big problems. The first and most urgent is that a crucial ally in the south, the former film star Jayalalitha, who faces serious corruption charges after her term as chief minister of Tamil Nadu, refuses to back him.
It was said that she wanted her proxies to be the ministers of finance and law; alternatively, that she wanted the dismissal of her deadly rival who now runs the southern state. Whatever it was, Mr Vajpayee refused to grant it, and Jayalalitha pulled her 27 MPs. Mr Vajpayee was left well short of a majority.
Last night the head of state, President KR Narayanan, met leaders of the other main groupings, Congress, the United Front (UF) and the two main communist parties, to see if they had any bright ideas. But as both Congress and the UF are effectively leaderless, and as it was their latest quarrel which brought on the recent, unwelcome election, no one was optimistic.
Mr Vajpayee's immediate problem stems from the treachery of a dubious ally. But his other problem is more fundamental: he has proved unable, after nearly 50 years of trying, to amass the sort of broad national support that the Congress Party used to be able to take for granted. The disputed religious site in Ayodhya, symbol of India and the world's doubts about Mr Vajpayee's party, continues to haunt him.
The BJP overflows with patriotic emotion; it stands for India strong, self-confident and with nuclear missiles targeting Peking. But in its heart of hearts India doesn't buy it. Ayodhya explains why not.
It is a small town in the fertile plains of Uttar Pradesh, east of Lucknow in the north of the country. To call it dilapidated would be a kindness: it looks like one of the frontline towns in Bosnia or Croatia in the heat of the recent wars there. It is a town of ruins, crumbling carcasses of long-ago invasions which the people inhabit without complaint, knowing nothing different.
But one of the ruins is special. It was demolished so thoroughly that not one stone remains on top of another. This was the mosque of Babri Masjid.
On 6 December 1992, a crowd of Hindu zealots, including the president of the BJP, LK Advani, Mr Vajpayee's right-hand man, and several of the party's MPs, gathered here and while police looked on they destroyed the mosque.
It was an explosive event, unleashing a volcano of Hindu versus Muslim communal anger in which perhaps 2,500 people died across the country. Mr Advani and several other top leaders were arrested, and the RSS, the paramilitary force that stands behind the BJP, was banned. But for the moment at least, Mr Vajpayee was unrepentant. Weeks after the demolition he declared that the mosque was "a symbol of shame and has been erased".
For the Hindu zealots, it was their movement's finest hour. But for Mr Vajpayee and the others in the party who crave national power it was, as Mr Vajpayee later admitted, "the party's worst miscalculation".
It is hard to grasp why the destruction of a seedy old building, unused for religious purposes since 1949, should dog the Indian imagination in the way it does. The ostensible reason is that the spot on which the mosque stood was the birthplace of Rama, "lord of the universe" in the Hindu pantheon and appropriated by nationalists as their divine mascot. Like thousands of Hindu temples across the north, it was destroyed by fanatical Muslims during the numerous invasions that wracked the country - supposedly in 1528, on the orders of Babur, founder of the Mughal empire - and replaced with a mosque.
The temple's erasure and replacement are conjectural as no archeological evidence has been found, but then so is the birth of Rama. When the abject and humiliated Hindus began chafing at the British yoke and casting around for a symbol of national pride to unify them 150 years ago, they hit on Ayodhya and the long-vanished temple there. Demolishing the mosque and rebuilding the temple have been the most important projects nursed by nationalists since.
Ayodhya has always been a potent rallying cry for the BJP. But the destruction in 1992 was a watershed. The symbol of national humiliation was gone - replaced by a makeshift temple in a tent, a messy ongoing wrangle in the courts, and a dire warning of the apocalypse awaiting any government that ventures down the communalist path.
The bloodshed that followed the mosque's demolition drove home the danger of igniting such raw emotion in a union as fragile as India's. But Mr Vajpayee has been unable to find any comparably effective way to set the electorate on fire.