That was welcome news to Liberal backbencher Tim Wilson.
"The Newspoll clearly shows that the prime minister is the government's strongest asset with the public in terms of the attitude and reception he receives," he told Sky News on Monday.
"It also highlights that the biggest problem the opposition has is Bill Shorten."
Despite splashing out on planned personal tax relief, the coalition still trails Labor 49-51 per cent on a two-party preferred basis, the poll published in The Australian shows.
A separate Ipsos poll published by Fairfax Media puts the coalition in an even worse position against Labor at 46-54 per cent, which is a decline from 48 per cent in April.
But Mr Turnbull did increase his Ipsos lead as the preferred prime minister to 52 per cent, against 32 per cent for Mr Shorten.
And asked if they thought they would be better off under the new budget, 38 per cent of the 1200 voters polled by Ipsos believed they would.
Some 57 per cent wanted the government to use the money to pay down debt, compared to 37 per cent who preferred to have income tax cuts.
The Newspoll of 1728 voters found 29 per cent thought they would be financially better off due to the budget measures, compared to 27 who thought they wouldn't.
A majority in this survey backed the income tax cuts plan.
Labor frontbencher Michelle Rowland believes as more people learn further details about the government's measures the numbers will change.
"As Australians start to realise the choices this government has made with this budget and contrast them to what Labor is offering I think they will come to see that the better deal is under Labor," she told Sky News.
"It will take some time for those messages to get out."
The polls follow separate income tax cut promises during budget week and a citizenship crisis that forced four Labor MPs to resign from parliament.
Both major parties are gearing up for a string of by-elections to be held across the country as soon as July.