Two key crossbench senators could support proposed income tax cuts provided the government promises that services won't be cut.
Centre Alliance's Rex Patrick said tax relief would be delayed beyond July 1, but raised the prospect of supporting the package when parliament returns.
"Centre Alliance would like hard-working Aussies to get a tax cut but in the face of a softening economy, we need to make sure that a year down the track we're not facing cuts in services, education or pensioner support," he told ABC radio on Wednesday.
"There is some chance that we will come to a conclusion that this is a good thing. We just have to do our due diligence."
Parliament can't sit until the Australian Electoral Commission returns the election writ to the governor general, which is due by June 28.
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The Australian Tax Office can retrospectively amend tax assessments to provide cuts if the laws pass after June.
Labor leadership hopeful and shadow treasurer Chris Bowen said the government had broken its first promise since being re-elected.
"A day after the election they have been found out about lying about tax cuts which was an essential part of their re-election agenda," he told ABC News Breakfast.
The opposition supports the first stage of tax relief, but it is unclear whether it will continue to oppose the second and third parts of the package.
"The best thing would be for the government to just separate those and allow its immediate passage through the House of Representative," Mr Bowen said.
"If they don't do that, then we'll have to consider our position, but they're playing games trying to cover up their lies during the election campaign."
The government looks set to rally crossbench support rather than split its package.
