The smiles on Spain's election night told part of the story. Although Socialist Prime Minister Pedro Sanchez came in second place in the vote and his ally Yolanda Diaz finished fourth with her new Sumar leftist alliance, they both wore big grins when addressing their respective supporters celebrating the results on Sunday evening.

But the election winner, the conservative Popular Party (PP) leader Alberto Nuñez Feijóo appeared less jubilant speaking to his large crowd of faithful, while third-place finisher, Santiago Abascal of the far-right Vox party, looked downbeat when he took to the stage.

No single party won enough parliamentary seats to form a government with a majority in Spain's 350-seat legislature. Feijóo's PP won 136 representatives, followed by Sanchez's Spanish Socialist Workers' Party (PSOE) with 122, then Vox's 33 and Sumar's 31. The complex process of horse-trading and negotiations to reach a minimum number of 176 deputies must now begin.

Sanchez had called this snap vote after his ruling coalition of left-wing partners suffered major setbacks in May's regional and local elections.

Since then, the Spanish left had warned voters that this election could put a far-right party into government -- with a PP-Vox coalition -- for the first time in decades. Vox takes a hardline on immigration and had pledged to roll back protections for women and LGBTQ people.

While some polls predicted Feijóo's conservative party would get close to a parliamentary majority on its own, voters instead left him 40 seats short. And even when combined with Vox -- which lost 19 seats from its showing in the 2019 election -- the duo would still be seven seats short of a majority.

"Spain has contained inflation and now it has contained the ultra-nationalist Vox party," Andres Villena, a professor at Madrid's Complutense University, told CNN Monday.

That's different than in some other European countries, where far-right parties have scored gains, now governing in Italy under Prime Minister Giorgia Meloni and entering the government in Finland.

In Spain, parliament is now due to convene in mid-August to select a new prime minister -- a process which includes the parties discussing their preferences and abilities to govern with King Felipe VI, the head of state. Spanish media reported that the contacts have already begun, just hours after the voting concluded.

Shaping up as potential kingmakers for any coalition government are the nationalist parties in Catalonia and in the northern Basque region.

Spanish media reported Monday that Feijóo says he'll talk to the Socialists about letting the conservatives govern. But Sanchez reportedly told aides that a formula will be found for a government without repeating the elections.

Villena said Feijóo could talk to the Basque Nationalist Party (PNV) who won five seats and, in Catalonia, the Junts party with seven seats, because their predecessors helped a previous conservative leader to govern. But Villena said that Feijóo's "scorched Earth" stance against independence for those regions could make negotiations difficult.

In addition, nationalist parties have expressed misgivings about joining a coalition with PP if Vox were involved. Vox's platform seeks a return of control to the central government from Spain's autonomous regions that for years have gained greater powers in policing, education and health. Its manifesto, for example, promised to replace autonomous regional police forces -- such as the Mossos d'Esquadra in Catalonia -- with national police.

Sanchez was with US President Joe Biden in the Oval Office in May, and earlier this month visited Ukrainian President Volodymyr Zelensky in Kyiv, where Spain has sent weapons and other aid. Having survived the election that he gambled his career on, analysts say Sanchez may be the best placed to renew a coalition government.

A coalition headed PSOE and Sumar may indeed have more routes to forming a governing alliance than one on the right wing, but it remains complicated.

A senior Socialist Party aide told CNN Monday that any Sanchez coalition deal "will be tougher this time, because the nationalist parties will ask a higher price."

The leader of Junts, Miriam Nogueras, said Sunday night in Barcelona: "We will not make ... Sanchez the next prime minister in exchange for nothing. Our priority is Catalonia, not the governability of the Spanish state."

But for Sanchez and Feijóo, running Spain is the priority. Sanchez, the incumbent leader, starts this coalition-building process after helping to successfully halt the advance of the far right. Meanwhile, Feijóo, the election "winner," must balance developing new potential partners with his thorny relationship with Vox.

There's a lot going on behind the politicians' smiles, and it could be weeks or months before we find out who will form Spain's next government.