Maduro, the unpopular inheritor of a socialist revolution, shows no sign that he will heed those calls.
"Maduro is trapped in an electoral maze of the regime's own making," Phil Gunson of the International Crisis Group wrote last month. "After years of using elections as plebiscites, confident that oil revenue and the charisma of the late strongman Hugo Chavez would always ensure victory, the Government can now - with Chavez gone - neither muster the electoral support nor find a convincing reason not to hold a vote."
And so the protests continue. Dozens have perished in clashes, and hundreds have been injured.
A small minority of demonstrators have resorted to violence as Maduro mobilised armed gangs of loyalists, known as "colectivos", to counter the uprising.
The security forces, my colleagues report, "appear increasingly determined to choke the protest movement with brute force, including the use of copious amounts of tear gas".
Several protesters have been killed or severely injured by gas canisters fired into crowds or allegedly dropped from government helicopters. Last week, a young man was injured when he was run over by an armoured police vehicle that ploughed through a melee.
In response, protesters have adopted some unusual tactics. Many sport armour and helmets retrofitted from household goods.
And, after being confronted by countless rounds of tear gas, some came to the streets on Thursday with a nasty new weapon: faecal matter.
According to a Reuters report, some protesters were making "poopootov cocktails" - plastic or glass jars filled with a mix of water and human excrement.
"The kids go out with just stones. That's their weapon. Now they have another weapon: excrement," a 51-year-old dentist said to Reuters while preparing containers of faeces in her home.
This revolting state of affairs is in part the consequence of a rolling economic crisis and recession.
Since Maduro took office in 2013, Venezuela's economy has cratered, inflation has soared and Venezuelans have endured serious food shortages and blackouts that shuttered hospitals.
Whole swathes of the population are reporting acute weight loss and a cutback in their daily meals.
This week, the Venezuelan Government published shocking new data: The country's infant mortality rate rose 30 per cent last year, maternal mortality shot up 65 per cent and cases of malaria jumped 76 per cent.
As Maduro extends the crackdown and even hauls civilians before military tribunals, there's a growing sense that external pressure is needed to ease the crisis.
All eyes are on a meeting of the Organisation of American States, or OAS, expected this month, where Venezuela will be at the forefront of the agenda. Maduro has threatened to pull out of the regional alliance, which is headquartered in Washington.
If he follows through, it would make Venezuela only the second country after Cuba not to belong to the hemispheric bloc.
"Venezuela is drowning in an economic, financial, social and humanitarian crisis of gigantic proportions," said Luis Almagro, the secretary-general of the OAS, in a recent interview with Bloomberg News. "There is a dictatorship in Venezuela, and Venezuela needs elections.
"The only institutional exit for the country is a general election."
Maduro has seen the erosion of his Government's base, with many of Venezuela's poor - once uplifted by "chavista" populism - suffering amid the wreckage of a collapsing state.
But he may now fear fractures within the ruling party and the waning support of the security services that guarantee his power.
"Maduro's plans for a new constitution will depend on the continued support of Venezuela's armed forces," the Washington Post's Nick Miroff wrote.
"It is not clear how the proposal will be received by other members of the 'chavista' movement - Chavez loyalists - who have become increasingly uncomfortable with the Maduro Government's more radical turn."
In the meantime, protesters will keep turning out in the streets of the country's divided cities.
