“The only true mandate is when voters give a single party control of both houses and that hasn’t happened in this particular instance,” Senator Griff said.
“So there’s really no such thing as having a mandate for everything you propose.”
Mr Morrison has moved closer to securing 77 of the 151 seats in the House of Representatives, with the Australian Electoral Commission shifting three seats out of its “close seats” tally on Monday.
The Coalition so far has 75 seats and is ahead in two others, Bass in Tasmania and Chisholm in the eastern suburbs of Melbourne, which are considered too close to call.
Labor has 67 seats and is ahead in Macquarie, in the Blue Mountains and Hawkesbury region west of Sydney, while the Greens have one seat and the remaining five will be held by smaller parties or independents.
Treasurer Josh Frydenberg is expected to head to Canberra on Tuesday for meetings with Treasury on the state of the economy and the budget agenda, while Mr Morrison has named the tax cuts as the priority when Parliament resumes within weeks.
Mr Morrison said on Monday that voters wanted the government to get “back to work”.
“They don’t want to see politics in their face or anything like that. They’ve had their say, they’ve made their decision. Now they expect us to get on with it so they can get on with their lives,” he told radio host Alan Jones.
“That’s what the ‘quiet Australia’ has said and I’m going to honour that.”
While the government must wait for the election writs to be returned in the weeks ahead, it is hoping Parliament can meet before June 30 to pass the first round of tax cuts, which are due to start on July 1.
Any delay to that timetable would force the Australian Taxation Office to back-date the tax cut in the new financial year, while also leaving the government exposed to attacks for taking too long.
The government is yet to make a decision on whether to split the $158 billion tax cut package from the April 2 budget into separate bills, a crucial move if it is to get swift approval in a Senate that has forced changes to its earlier tax cuts.
The most likely option is to break up the tax plan to ensure it can legislate the immediate tax cuts, including a tax offset worth $1080 for workers earning between $48,000 and $90,000 a year.
The plan includes smaller benefits for those earning below $48,000 and those earning up to $126,000 a year.
While Labor offered a bigger tax offset for workers earning up to $48,000 a year, it is expected to legislate the first stage of the government tax cut if the budget plan is split into separate bills.
The latest election count has confirmed earlier signs that the Senate crossbench will include Senator Hanson and her One Nation colleague Malcolm Roberts, as well as the Australian Conservatives’ Cory Bernardi and Tasmanian independent Jacqui Lambie.
Combined with Senator Griff and Senator Patrick from Centre Alliance, this suggests there will be six on the crossbench and the government will need support from five of them to pass contested legislation.
Most senators elected on Saturday take up their positions from July 1, changing the numbers on the crossbench and ending a period when the government needed nine out of eleven crossbench senators to pass any bill opposed by Labor and the Greens.
Senator Hanson’s party has blocked some of the government’s income tax cuts in the past over concerns that the benefits for wealthier workers were too costly, and is yet to decide its position on the $158 billion package announced on April 2.
“We will familiarise ourselves with stages one, two and three [of the tax cuts] and have discussions with the appropriate ministers over the following few weeks,” a One Nation spokesman said.
Senator Griff said the government could not claim a mandate for the tax cuts or other policies when almost 60 per cent of voters did not give the Liberals their first preference.
“We’ll work respectfully with them to progress their key policies but we’ll always look at whether the outcomes are positive for South Australia and it’s important that the end result won’t be any form of degradation to core community services,” he said.
On tax cuts, for instance, the Centre Alliance position is that there can be no impact on the budget that would force cuts to services.
The Grattan Institute estimated during the election campaign that the government plans would require spending cuts of $40 billion by 2030.
“What we supported previously was part one and part two [of the tax cuts] and we didn’t support part three,” Senator Griff said.
Senator Patrick said the key issue was looking after South Australians and government services.
“When we look at these things, we look at how we can preserve services,” he said.
“So it could be a case where we support stages one and two but not three.”
Senator Bernardi said he was “100 per cent” behind the income tax cuts and praised Mr Morrison for defeating a Labor Party that prosecuted a form of “class warfare” during the election campaign.
“The fact that he won provided a clear verdict,” Senator Bernardi said.
“For the first time since Tony Abbott led the government, I think the Coalition presented an alternative vision to Labor for the country.
“I think voters did not want big government or the nanny state, so full marks to the Prime Minister, he did a great job, even if he snaffled all of our voters.”
David Crowe is Chief Political Correspondent for the Sydney Morning Herald and The Age.