Prime Minister Malcolm Turnbull has used the poll, in which about two-thirds of voters endorsed key measures, to argue the Senate crossbench should pass those policies because voters had given them the "tick of approval".

Former prime minister Tony Abbott gave the Turnbull government's second budget a more lukewarm endorsement, however, describing it as "the best the government can do in the circumstances" while blaming the Senate for a series of tax hikes.

The May budget unveiled a $6.2 billion tax increase on Australia's five largest banks, a 0.5 per cent rise in the Medicare levy from July 2019 to fund the National Disability Insurance Scheme, an $18.6 billion, 10-year increase in school funding, and a boost to infrastructure spending funded by a larger national debt.

The Coalition's primary vote rose four points in the Fairfax-Ipsos poll, while Labor's rose by one percentage point.

The federal opposition still holds a strong 53-47 lead in the two-party preferred vote, though that lead fell back from 55-45 in the March Fairfax-Ipsos poll, based on 2016 election preference flows. On stated preferences, the change was a net 6 percentage point improvement for the Coalition, also to 53-47.

Labor's lead in Monday's Newspoll was also 53-47, up from 52-48 in the previous poll.

Fairfax-Ipsos pollster Jessica Elgood said the budget had delivered a small improvement in the polls for Mr Turnbull and Treasurer Scott Morrison.

"We have seen a statistically significant shift in the stated preference votes, they [the Coalition] picked up three points and that is backed up by Turnbull's approval rating and strong support for the budget measures. Plus, a majority of people think the budget is fair," she said.

"It's not a big move, it could be thrown away, now they have to back it up and follow through."

Queensland Liberal MP Warren Entsch said the budget had given the Coalition a platform on which to rebuild its fortunes, but added "now we have to deliver on it. We have to implement these policies."

NSW Liberal MP John Alexander said it would take a month or more for people to digest the budget's major measures properly but the poll result was welcome.

Mr Alexander, who championed policies to improve housing affordability, said the steps taken in the budget were a "good start" but more needed to be done.

Several other Coalition MPs from across the country, who asked not be named, said they had not expected a big boost in the polls from the budget but, as one put it, "we can build on this. We have to get out there and sell it and highlight how bad it would be if Labor was elected to government."

The Prime Minister, meanwhile, said the most important message from the two polls was that "people think it's [the budget] fair".

"They support the major bank levy by a very big margin. They support the adoption of the Gonski formula and a fair, needs-based approach to school funding by a big margin and they support the Medicare Levy increase by a very big margin," he told radio station 2SM.

"Now what that means is that the budget has got a big tick of approval...we want the [crossbench] senators to listen to that, the sentiment that's being reflected from the public, and support all those measures when they come to the Senate."

Mr Abbott described the Senate as a "house of rejection, not a house of review", and called for reform of the upper house that would stop legislation being blocked indefinitely via a change that would allow a joint sitting without a double-dissolution election.

"We would have liked to have had a savings budget, [but] the Senate doesn't like savings budgets as they showed in 2014, so instead we have got a taxing budget. This is the best the government can do in the circumstances."

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