Across Spain, everyone has an opinion about Pablo Iglesias. Mere mention of the ponytailed leader of the insurgent leftwing party Podemos (We Can), who is only 35, elicits a barrage of adjectives that range from honest to dangerous.

There was the woman in Barcelona who gushed that "he seems like such a decent person" as she explained why she had cast her first vote in a decade and given it to Podemos. Or the worries expressed by the monarchist from San Sebastián who spent hours waiting on a sunny morning in Madrid to catch a glimpse of Felipe VI on his first day as the new king of Spain. "Iglesias wants to turn Spain into the next Venezuela."

In only a month, Iglesias has gone from well-known political pundit to member of the European parliament and one of Spain's most polarising personalities. Soft-spoken and calm, Iglesias shrugs off the attention. "I'm a normal person," he said. Active in left-leaning politics since he was 14, he describes himself as "a guy who worked in the university for many years, as a researcher, then as a professor".

Wearing a shirt lined with the red, yellow and purple colours of the Spanish republic, Iglesias pulled loose his ponytail as the interview started, his long brown hair falling over his shoulders for a moment before he tied it back into his signature style.

Sleep, he said in a voice tinged with exhaustion, had been hard to come by recently, lost amid a whirlwind of press conferences, party meetings, travels back and forth to Brussels in his new role and media appearances. "Very intense" is how Iglesias described the last month. "The truth is that ever since the election we've been overwhelmed by the response, the media attention, the hope of the people. But we're very hopeful because we think that we're contributing to something historic – the political change in our country."

A month ago Podemos came seemingly out of nowhere to capture 1.2 million votes and five seats in the European elections. Registered in March this year with the intention of turning the anger of Spain's indignados into real political change, Podemos became the third political force in many regions of Spain, including Madrid.

The anti-austerity party's list of election promises includes higher minimum wages, doing away with tax havens and EU border controls, the nationalisation of utilities and banks that were rescued with public funds, establishing a guaranteed minimum income and lowering the retirement age to 60.

While the elections saw many countries turn to Eurosceptic parties, many Spanish voters turned sharply left, harvesting votes from the country's two dominant parties in the wake of an economic crisis and years of corruption scandals. The governing People's party and the Socialists received less than half of the vote, a far cry from the 81% support they got in 2009.

The day after the election, Socialist leader Alfredo Pérez Rubalcaba said he would be stepping down. A week later King Juan Carlos announced he was abdicating in favour of his son, Felipe. Both changes, according to analysts, were rooted in the clear demand for change expressed by voters in the European elections.

For Iglesias, it's the beginning of the end for the regime that has governed Spain since 1978. "In some ways, it's their institutions that are in crisis: a monarchy that's more and more identified with impunity and corruption and the established political caste of the regime." The goal of Podemos was to turn the social majority into the political majority, said Iglesias, by having ordinary citizens do politics. "If people don't do politics, others will do it for you. And when others do it for you, they can steal your rights, your democracy and your wallet."

Solutions for the country, Iglesias has insisted repeatedly, come not from the adherence to leftwing or rightwing ideology, but rather in a movement against a privileged elite whose priorities are out of synch with what is best for most Spaniards.

The party's success came earlier than expected, sending the Podemos leadership scrambling to formalise the movement and prove it is more than just a phenomenon fuelled by protest votes. Lacking member lists, leadership to inform on day-to-day decisions and a system to hold its MEPs accountable, Podemos is now on a quest to find a balance between being a grassroots movement informed by a loose network of hundreds of working groups across the country and a functioning political party.

The clash between the two priorities was on display last month after Iglesias announced he was nominating a list of 25 people to organise a general assembly in the autumn and gave others six days to present competing lists. Some grassroots members criticised what they saw as an affront to Podemos's open structure.

It is still not clear how the party will work. Many of the answers, said Iglesias, would come in October at a general assembly where the emphasis would be on designing tools that allowed the party to respect its participative style and commitment to direct democracy. Critics suggest the emphasis on participation might be the party's achilles heel, in that it leads to ideas that, while popular, may not be workable. Others question the ability of Spain's fragile economy to withstand deep changes as it emerges from a long recession.

Iglesias brushed off these worries. "You can't be scared of democracy. These arguments that participation can be contradictory with efficiency is contrary to the very idea of democracy." He likened it to critics of universal suffrage who argued that it would cause chaos if everyone were able to vote. "We've seen that this isn't true."

In a country where one in four is unemployed and more than 150,000 families have been evicted from their homes in the last five years, Iglesias argues that pragmatism is relative. "It's not realistic that we have six million unemployed and that you can be poor even if you have a job," he said. "Our measures aren't very radical. They are measures that are very prudent along the lines of a project to save the country in the face of a crisis."

Polls suggest the party is gaining ground, showing that it could win between 30 and 58 seats in the Spanish parliament and capture as much as 15% of the vote, almost double the percentage it received in the European elections.

But as Podemos rises in the polls, so does scrutiny of Iglesias. He has been compared to Adolf Hitler and Fidel Castro and called a freak and extremist. Others have taken aim at his words – he has been accused of justifying terrorism at the hands of Eta after he said that the group's violence "had political explanations" that needed to be understood in order to find democratic solutions.

At times the attacks had been amusing, he said, pointing to those who took aim at the fact that he bought his clothes at a low-cost supermarket. "I never thought it would be a subject of interest or that it would generate so much controversy," he said, smiling.

The attacks neither surprise nor bother Iglesias. To him, it is a demonstration that Podemos is making those in power nervous. "That's why they insult, defame, scream. It's a sign that they're worried."

Now the pressure is on for one of Spain's most polemical politicians to turn that worry into real political change. While he refused to rule out leading the country one day, Iglesias said his focus now was on political contribution.

"We want a more decent country. A country with public services, a country where nobody is thrown out of their house, a country with public hospitals, public pensions, a country in which if you have work you can fill the fridge and buy school supplies for your children," he said. He shrugged as he added: "Just the simple things."