Crossbench senators would support the government’s $175 billion tax plan in exchange for a tax on digital companies such as Google, Facebook and Uber.

The government needs two more votes to get its plan to cut income tax for lower- and middle-income earners and lower the corporate tax rate passed in parliament.

Centre Alliance senators Stirling Griff and Rex Patrick were “100 per cent behind a digital economy tax proposal”, Fairfax Media reported Monday.

“If the digital economy tax makes the government coffers swell more than they do now, that is very much a positive step,” Senator Griff was quoted as saying.

“As long as there are no cuts to core community services, we’d be receptive to a degree of tax relief for everybody. A lot could happen in six weeks; maybe the company and income taxes can be done by July.”

The government is trying to get its $140 billion income tax cut plan through parliament as well as its $35.6 billion bid to lower the corporate tax rate for big businesses.

However, the Greens have said they won’t support it, whether or not the Turnbull government caves in and splits its seven-year personal income tax plan.

The package, a key plank of this month’s federal budget, is due for debate in House of Representatives on Tuesday.

Labor supports the first part of the tax cut plan which starts with a reduction of up to $530 a year under a low and middle-income tax offset.

If it wins the next federal election, Labor has promised almost doubling this offset to over $900.

But it won’t back the Turnbull government’s second and third steps, which make changes to certain tax brackets at various stages, until at least the government provides more information on their cost.

The budget papers show the plan will cost $13.4 billion over the first four years, but Treasurer Scott Morrison has repeatedly declined to break it down year-by-year beyond that other than to say it will amount to $140 billion over 10 years.

Mr Morrison is also adamant he won’t split the package to ensure its passage in the Senate where the government doesn’t have a majority.

But the Greens won’t have a bar of any income tax cuts from either of the major parties.

Greens leader Ricard Di Natale believe these tax cuts are no more than a bribe by the government to gain support for the remainder of its company tax cuts which are stuck in the Senate.

He says the priority should be greater investment in public services.

“For years, politicians have been telling Australians that the budget doesn’t have money to properly fund our public schools, build a world-class NBN, or take action on climate change,” Senator Di Natale told AAP.

“Yet when an election is rolling around both old parties are giving away cheques like a breakfast TV show trying to increase their ratings.”