A straw poll of Greek voters at one centre in Athens suggests many do see the local elections as a referendum on the austerity cuts.
While some want to encourage George Papandreou to press ahead, others are scathing.
“I voted with the intention of showing the government that I am against the measures it has taken,” said Angelos Sofianopoulos, after casting his ballot.
“We have to give a vote of confidence to the government,” said a woman, who gave her name only as Anna. “They are working for us. They are not cheating us. I see the situation is difficult. We have to do something for the economy.”
However some are angry that the nation’s economic strife is dominating debate in what are, after all, local elections.
“People are so enraged with all the parties that they have placed huge importance on this issue. It should not be this way. It should be what each citizen decides for his own neighbourhood,” said Maria, outside a polling station in the capital.
The Socialists came to power last year and enjoy a comfortable parliamentary majority. National elections are not due in Greece until 2013.