In a clear sign the federal government is adjusting its overarching budget strategy, Prime Minister Tony Abbott and Finance Minister Mathias Cormann both held out the prospect of policy ‘‘adjustments’’ at the weekend to smooth the passage of key budget measures.

Key crossbench senators said they could work with the government on a revised Schoolkids Bonus and unanimously called for the mining tax repeal bills to be split, allowing the tax to be axed but some spending measures to be kept.

Ms Bishop, who will on Monday launch Australia's economic diplomacy agenda, said the government had already compromised to repeal the carbon tax and pass changes to financial advice laws, and further compromise was needed.

‘‘I look back at the GST that John Howard took to the 1998 election. We won that election with a very detailed plan to introduce a GST. Yet we still had to compromise to get it through the Senate,’’ she said.

‘‘I see that as an indication of the need to compromise to achieve your aims, even after an election.

‘‘In the case of the mining tax, it’s clear that it’s a useless tax ... the mining tax must go. The question, is how do you pay for the benefits that Labor promised would come from the mining tax?’’

Liberal backbenchers said it was ‘‘stating the bleeding obvious’’ to say the budget would have to be changed to pass through the Senate.

On Monday, Ms Bishop again called for compromise with the crossbenchers, saying if they had constructive suggestions to make ‘‘we should consider them’’.

She denied the government had failed to sell the budget and said the Coalition had moved on from Treasurer Joe Hockey’s damaging poor-people-don’t-own-cars comment.

'‘It’s always going to be difficult to sell a budget in the first term,’’ she told ABC radio. ‘‘Previous governments have found that difficult and we didn’t ever think it was going to be easy with this budget.’’

She also said it was ‘‘early days’’ in the government’s efforts to get its budget through parliament.

‘‘I know budget measures have taken years to get through in previous governments,’’ she said.

The government failed to repeal the mining tax in the last parliamentary sitting because the Palmer United Party insisted, along with Labor and the Greens, on keeping the Schoolkids Bonus, income support bonus and low income superannuation contribution.

Those three measures will cost the budget about $1.7 billion in 2014-15 and nearly $10 billion by 2017-18 if retained. The total cost of the mining tax-linked spending measures is just over $17 billion over four years.

Cabinet will meet on Tuesday in Melbourne. Budget strategy is expected to feature prominently after a horror week for Treasurer Joe Hockey, who issued a grovelling apology after declaring the ‘‘poorest people don’t drive cars’’ while arguing the case for a rise in petrol excise.

Senior government sources played down suggestions of a full-blown budget ‘‘reboot’’ but confirmed a pragmatic shift was under way before Parliament resumes next week.

The shift could see ‘‘adjustments’’ made to about $40 billion in proposed savings and revenue measures blocked by the Senate, including the fuel excise, the $7 GP co-payment and changes to tertiary fees.

Independent South Australian senator Nick Xenophon said he was open to making the Schoolkids Bonus more tightly focused on education spending.

Amending the scheme, rather than ditching it all together, would be a welcome ‘‘pragmatic’’ move but Senator Xenophon said the government's budget problems were ‘‘more deep-seated than that".

''Talk of a reboot shows what a mess the budget is – there needs to be a mini budget,'' he said.

On Monday, MP Clive Palmer again labelled the budget unfair, saying it was not something his senators could support.

Asked how the government had handled the sales job, he said: ‘‘Not very good’’.

‘‘Because nothing’s happened - nothing’s passed,’’ the Palmer United Party leader told ABC radio.

Opposition Leader Bill Shorten said the budget needed more than a '‘new coat of paint’’.

‘‘Tony Abbott needs to tear it down and start again ... he needs to back down on the unfair measures in his budget.’’

with AAP