His right-wing People's Party (PP) still won the most seats in parliament, 129 - but that was far down from the 176 seats it would need for an absolute majority, let alone the 186 it had before the election.
Pablo Iglesias, the man who founded the Podemos (‘‘We can'') party only two years ago, agreed with Mr Rajoy on this, if on little else. ‘‘Ladies and gentlemen, this is the captain speaking in the name of Podemos,'' he told a rally during the campaign.
‘‘We thank you for choosing the path of change. We're expecting a bumpy ride with political turbulence.''
Podemos ended up with 69 seats, not bad for a two-year-old party in its first national election - but it doesn't seem interested in co-operating with the other left-wing party.
‘‘Hopefully, Podemos would be willing to work with us,'' said Juan Fernando Lopez Aguilar of the Spanish Socialist Workers' Party (PSOE), which got 90 seats, ‘‘but so far I perceive a threatening mixture of arrogance, self-infatuation and condescension.''
‘‘If the socialists or PP had done nothing wrong, neither Podemos nor us would exist,'' Albert Rivera, leader of the even newer party, Ciudadanos (Citizens), said.
Last January, it was barely known outside Catalonia, with only 3% support in the polls. Last Sunday, Ciudadanos got 14% of the national vote and 40 seats. So forming a new government in Spain is going to be a long and messy process.
The PP and the PSOE alternated in power, and during the three-decade boom after Spain joined the European Union, nobody much minded the lack of viable alternatives. Then came the world financial crisis of 2008, with stagnant or falling wages for most Spaniards and an unemployment rate that reached 27%.
Each party had a turn at trying to deal with the crisis, and each cut the national budget, rescheduled or repaid as much debt as possible, and imposed severe austerity. Even Spain's population began to fall, as the young left in droves to find work elsewhere in the EU.
So there was plenty of room for a new party offering an end to austerity, and for a while it looked like Podemos was it. It was anti-capitalist, its 36-year-old leader wore a pony-tail, and it promised radical change. Some people worried it had ‘‘Venezuelan'' tendencies, but a year ago the polls suggested it could even come out ahead of both traditional parties.
Not so fast. Since January, the other new party, Ciudadanos, has been pulling away the more nervous among the mass of disaffected voters who were once willing to back Podemos. Ciudadanos also has a 36-year-old leader (no pony-tail) who talks about radical change, but it is really a centre-right party that sits comfortably in the middle of the road, long left empty by the traditional parties of left and right.
That split the protest vote, so now Spain has four major parties, and creating any sort of coalition government is going to be very hard.
The arithmetic means either the PP or the PSOE must be in any coalition that can command a majority in parliament, but Ciudadanos swears that it will not join any government that it does not lead.
Podemos is being equally difficult, saying that it will ask its supporters to vote on joining any coalition. (Being fed up with both traditional parties, they would probably say no.)
So unless there is a ‘‘grand coalition'' between the PP and the PSOE - which is also very hard to imagine - it may not be possible to form a new government at all. In which case, after two months, there must be another election - and you can forget the economic recovery.
Hard times do not usually make people more moderate and open to compromise. Spain is a perfectly reasonable country that has managed its democracy well for 40 years, but it may just have made itself ungovernable.
● Gwynne Dyer is an independent London journalist.
