The poll, published in the To Vima newspaper, showed 46.6 percent of 1,044 people surveyed backed fiscal measures that include 4.8 billion euros ($6.5 billion) in new savings and tax hikes, while 47.9 percent disapproved.
The survey suggests the government cannot expect an easy ride in pushing through its consolidation drive.
But protests have been much more low key than the riots seen in Greece in December 2008. Police estimated that about 12,000 people had taken part in the Friday marches in Athens, a small fraction of the capital's population of 3 million.
Saturday's survey came after European leaders expressed confidence on Friday that the new measures would be enough to pull the country out of a budget crisis that has shaken the 16-nation euro zone and make any bailout unnecessary.
Greek Prime Minister George Papandreou received political support but no promise of any specific financial aid at talks with Chancellor Angela Merkel in Berlin and with Eurogroup Chairman Jean-Claude Juncker in Luxembourg.
But French President Nicolas Sarkozy made clear in remarks on Saturday that Paris stood ready to help Athens if its financial situation were to deteriorate further.
Papandreou is due in Paris on Sunday to meet Sarkozy as part of a tour to seek backing for his country, whose debt has swollen to about 300 billion euros, well above its annual economic output.
"If we created the euro, we cannot let a country fall that is in the euro zone. Otherwise, there was no point in creating the euro," Sarkozy said at a meeting with farmers. "The euro has no sense if there is no solidarity,"
The Saturday poll, carried out by Kapa Research, showed most Greeks opposed measures immediately affecting them, such as a 2 percentage point rise in value added tax (VAT), a 30 percent cut in public sector holiday bonuses and a pension freeze.
But about nine out of 10 appeared to strongly support salary cuts for senior officials and civil servants. The findings echoed a survey published on Friday which showed strong opposition to some elements of the belt-tightening package but support for others.
Two opinion polls published in late February, before the new fiscal measures were announced this week, showed just over half of Greeks believed the government was tackling the crisis effectively.
Analysts say the government has relatively high levels of political capital after winning a snap election in October.
Papandreou's socialist PASOK party has 160 out of 300 seats in Parliament and replaced a conservative administration accused of concealing the full extent of Greece's economic woes.
Ratings agencies and other EU governments have said ability to deliver will be key to determining whether Greece can re-establish its credibility diplomatically and as a borrower.
Economists also say the performance of the Greek economy, and the extent to which the cuts hamper any recovery from recession, will be a major risk in the coming months.
"The choice facing all Greeks today is collapse or rescuing Greece," Labor Minister Andreas Loverdos said in an interview published in the Greek Isotimia newspaper on Saturday.
Police said about 12,000 demonstrators took to the streets to protest against the new package on Friday when lawmakers passed the austerity measures in an emergency vote.
The main public sector union ADEDY brought forward a planned national strike to March 11 from March 16 and its sister private sector union GSEE said it would join them. The two unions represent half Greece's 5-million work force.
Workers spent the night boarding up broken shop windows and painting over graffiti in Athens after the protests but the levels of opposition to the government and the cuts have so far been relatively muted by both Greek and European standards.
In Ireland, which has also slashed spending aggressively but did so much more quickly, some 100,000 protesters last year marched through Dublin, which is one-third the size of Athens.
The latest protests in Greece have been far less violent than those seen in December 2008, when dozens of people were injured, hundreds arrested, scores of shops destroyed and more than 15,000 police deployed on the streets of Athens alone.
