Turnbull on Saturday announced more than a dozen changes to his ministry, a decision forced on him by the resignation of one minister, the retirement of two others and the sacking of two more over their involvement in political scandals.
A Fairfax-Ipsos poll of 1403 people taken on Feb. 11-13 showed the governments worst numbers since Turnbull ousted Tony Abbott in a party coup last September, narrowing its lead over the centre-left Labor Party by four percentage points to 52 to 48 percent.
A hostile upper house Senate continues to stymie any major policy moves and Turnbull is facing rearguard action from his partys conservative wing despite sticking to Abbotts unpopular stances on same-sex marriage and climate change.
An early election may be Turnbulls best chance to demonstrate bold leadership and reverse what seems to be a growing sense of buyers remorse, said Peter Chen, a senior lecturer in government at the University of Sydney.
"If youre going to follow Tony Abbotts agenda, then why did you roll him in the first place? It seems purely motivated by personal factors," Chen told Reuters.
"I ... think that the early election is the more likely possibility," he said after the poll was released.
Plummeting commodity prices have depleted the governments coffers, a major financial stumbling block for Turnbull, whose rise was sparked partly by his image as a prudent financial manager based on his background in the private sector.
Australia in December forecast its budget deficit would swell to A$37.4 billion ($26.6 billion) in the year to June as falling prices for key resource exports open a gaping hole in tax revenue.
Turnbull last week raised the possibility of an early election after ruling out a rise in the Goods and Services Tax (GST) under pressure from within his own party, despite strong support from economists.
The governments ability to have a stimulatory budget prior to the election is constrained by the size of the budget deficit, said Shane Oliver, Chief Economist at AMP Capital Investors.
"It has got its hands fairly well tied. Overall revenue remains under threat and the government doesnt like the idea of increasing government spending, so its not going to have a tax and spend set of policies going into the election," he told Reuters.
"The ditching of the GST as an option suggests that maybe structural reform is off the table."
($1 = 1.4049 Australian dollars)
(Reporting by Matt Siegel; Editing by Richard Pullin)