The future of the Coalition's $158 billion income tax cut package now rests in the hands of the Senate, having sailed through the House of Representatives without objection from Labor.

Key points: Now that the bill has passed the House of Representatives, the final hurdle is the Senate

Now that the bill has passed the House of Representatives, the final hurdle is the Senate The income tax cut package is slated to be considered by the Senate on Thursday

The income tax cut package is slated to be considered by the Senate on Thursday The Coalition needs four of the six crossbench votes for it to pass as it does not have Labor or the Greens' support in the Senate

The Government's three-stage plan passed the Lower House late on Tuesday night.

Labor did not vote against the package, believing it had a better chance of amending the bill in the Senate.

The Opposition supports the first two stages of the plan, which includes tax cuts for low and middle-income earners, but has refused to support the third stage, which involves long-term structural tax change.

Labor also wants the second stage — which addresses bracket creep — delivered earlier than planned.

It moved to introduce amendments to the bill to address those issues, with Shadow Treasurer Jim Chalmers telling Parliament the proposed changes would see millions of Australians get immediate tax relief.

"Every worker in the Australian economy deserves to have a tax cut from this week in this parliamentary term and not on the never never," he said.

"Our position is based on a reasonable, rational, hard-headed assessment of the economic and budgetary conditions under this third-term government," he said.

Jim Chalmers said the proposed changes would result in tax relief for millions. ( ABC News: Matt Roberts )

What's in a name? Frydenberg accuses Labor of mocking Australians

At one point during the debate, Labor even tried to change the name of the bill, which is called: "Treasury Laws Amendment (Tax Relief so Working Australians Keep More of Their Money)."

Opposition Leader Anthony Albanese moved it be amended to read: "Treasury Laws Amendment (Tax Relief So Working Australians Keep More of Their Money But Not For a Really Long Time)."

That prompted Treasurer Josh Frydenberg to hit back on the floor of Parliament.

"We won't join the Labor Party in mocking Australians, Mr Speaker," he said.

The Coalition rejected all of the Opposition's amendments, telling Parliament the public wanted the entire package, as it was promised.

"We won't join the Labor Party in making light of the fact that hard-working Australians are counting on this Parliament to pass our tax package in full.

"We oppose these amendments, these hastily cobbled together amendments, to create for the Labor Party some veneer of credibility."

Josh Frydenberg said the Labor Party had "mocked Australians". ( ABC News: Matt Roberts )

The final hurdle

The Senate will consider the bill on Thursday, with condolences for former Labor prime minister Bob Hawke the sole item of business today.

Without Labor or the Greens' support in the Senate, the Coalition needs four of the six crossbench votes.

Jacquie Lambie said she needed more time to determine whether she would back the cuts. ( ABC News: Matt Roberts )

Earlier in the day, returning Tasmanian senator Jacqui Lambie — who is likely to be a deciding vote — said she needed more time to determine whether she would back the income tax cut package in full.

"We only started on Monday. I've done everything I can in the last few weeks but I didn't have access to certain things so I'm working on that now," she said.

"Mate, I didn't have all the information on the table, still waiting for that information to come through so I'm not going left or right on this."

Independent senator Cory Bernadi will support the bill, while One Nation leader Pauline Hanson — who controls two votes on the Senate crossbench — has said she will not support the full tax cut package.

Centre Alliance holds two crossbench votes and has indicated it is likely to support the plan in full.

The Government is threatening to sit late on Thursday to deal with the bill, in order to pass it this sitting week.