The Centre Alliance party is leaving no stone unturned as it considers whether or not to back the federal government’s promised tax cuts when they come before the upper house.

The centrist minor party, formerly known as Nick Xenophon Team, is in line to hold two seats in the Senate, after the May 18 election, which means it could play a key role in getting the planned tax cuts across the line if Labor doesn’t back them.

Centre Alliance Senator Rex Patrick says he and his upper house colleague Stirling Griff would like nothing more than to give hard-working Australians a tax break.

But given the coalition government’s tax package will cost $158 billion in coming decades, their decision won’t be made lightly.

“I met yesterday with the Reserve Bank governor, I met with Treasury officials yesterday, and indeed had a lengthy conversation with (competition watchdog chairman) Rod Sims,” Senator Patrick told ABC’s Radio National on Wednesday.

“We are going through due diligence to make sure that whatever way we cast our vote, it is done on merit and on proper analysis.”

The tax cuts should have a clear run in the lower house, where Prime Minister Scott Morrison is set to govern with a 77 seat majority after two close-run seats were finalised on Tuesday.

But with Senate vote counting continuing, the 76-seat upper house to start on July 1 is likely to comprise 35 coalition MPs, 26 Labor, nine Greens, two One Nation, two Centre Alliance, one Australian Conservative MP and Jacqui Lambie from Tasmania.

Whether the tax cuts will get Labor’s backing remains to be seen.

The opposition supports the first part of the government’s tax plans, which will provide more tax relief for low and middle-income earners.

But it’s unsure about the later stage of the government’s package, which will flatten the tax rates schedule by mid-2024.

The coalition has ruled out breaking up the legislation, which will come before parliament next month.

Shadow treasurer Jim Chalmers was tight-lipped about the party’s position, after saying it would be high on the agenda when Labor’s frontbenchers met on Tuesday.

“If they did split the bill, we would enthusiastically pass the first tranche of tax cuts, which favour people on low and middle incomes,” he told the ABC following the meeting.

“We also need more information on the rest of the tax package.”