But economists point out there was an even bigger influence from a plunge in global oil prices.
Petrol prices have dropped below $2 a litre in most jurisdictions across the country, coming less than a week after Treasurer Josh Frydenberg slashed fuel excise to assist with cost of living pressures.
The national average petrol price in the past week fell by a record 13.3 cents to 193.4 cents a litre, Australian Institute of Petroleum figures show.
Only Tasmania and the Northern Territory were still recording prices above the $2 mark.
As part of an $8.6 billion cost-of-living package, Mr Frydenberg halved fuel excise to 22 cents a litre for six months after petrol prices surged to record highs as a result of a spike in global oil prices due to the war in Ukraine.
However, at the time of handing down the budget last Tuesday, the treasurer did warn that the reduction could take a couple of weeks to feed through the system.
"We are already seeing those lower fuel prices find their way to the bowser, which means Australians are already receiving the benefits of a budget handed down less than a week ago," Mr Morrison told reporters in Melbourne.
"I welcome that and I thank the petroleum industry for passing through those savings so quickly."
However, Commonwealth Securities senior economist Ryan Felsman said an even bigger influence has been the sharp fall international oil and fuel prices.
"International crude oil prices – the biggest influence on Aussie petrol prices – plunged last week," Mr Felsman said.
"Unleaded petrol prices are expected to fall further this week."
The Brent crude oil price plunged by $US16.26 a barrel, or 13.5 per cent, to US$104.39 a barrel last week.
Still, in further positive news for a government struggling way behind in opinion polls ahead of the May election, new job advertising figures suggest the unemployment rate could be in the "low threes" by the end of this year.
The ANZ jobs ad series produced a 0.4 per cent increase in March, coming off an upwardly revised 10.9 per cent gain in February.
Job ads are now 57.5 per cent higher than their pre-COVID-19 levels in January 2020.
Other recent gauges for worker demand have been equally upbeat.
Treasury expects the labour market to tighten further, forecasting the unemployment rate to reach 3.75 per cent in the September quarter and remain there until the middle of the decade.
"We are more optimistic, forecasting an unemployment rate in the low-threes by the end of this year," ANZ senior economist Catherine Birch said.
She said this presented upside risks to the budget's revenue forecasts.
The jobless rate currently stands at a 14-year low of four per cent.
Some economists expect a sub-four per cent unemployment rate could come in the March labour force figures due on April 14, which would be the lowest level since 1974.
Meanwhile, the Australian Bureau of Statistics confirmed retail trade grew by 1.8 per cent in February in an update release on Monday.
Figures originally posted last month showed sales rose to $33.1 billion in February, which was the second-highest month on record with spending regaining momentum after the Omicron variant outbreak peaked.
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