Jacqui Lambie, Rex Patrick and the Greens slammed Labor's decision to not back an amendment to a COVID-19 assistance bill, which would make a public database to show which companies took JobKeeper and made a profit.

The bill is part of a larger COVID-19 assistance package for businesses impacted by lockdowns around the country. Senator Patrick's proposed amendment was to create a public register similar to the New Zealand model, which shows how much taxpayer money was provided to support businesses.

Labor finance spokeswoman Katy Gallagher confirmed Labor would not oppose the bill, claiming the priority was to ensure rapid support was available to businesses impacted by lockdowns.

"Labor will not create uncertainty for these businesses," she said. "Before I hear the squeals from the crossbench, I doubt very much that any of them engaged with businesses or any employee that is currently locked down in these jurisdictions."

Following her comments, Senator Lambie lashed out at the ACT senator, saying her comments were offensive and the Delta outbreak was having a "domino effect" nationwide.

"Don't talk to me about small business," Senator Lambie shouted across the chamber at Senator Gallagher. "I am watching a West Coast town [in Tasmania] where 70 per cent of the damn street is closed down, so we are all feeling it. Let me tell what those small businesses want: transparency. They want to know why they are on their knees ... out there and big boys like [Gerry] Harvey have had all these extra JobKeeper payments. It's a whole domino effect and we are all feeling it whether it's in Canberra or Tasmania."

During the pandemic, a number of large publicly listed companies reported huge profits while taking JobKeeper and then went on to pay large dividend and corporate bonuses.

Retailers such as Harvey Norman have refused to give back JobKeeper payments despite posting record profits.

Ms Gallagher noted Labor would find other avenues to increase transparency around which businesses rorted JobKeeper.

"[The government] should have done it when it reviewed JobKeeper," she said. "Shine a light on it. Provide that information to tax payers who for generations will be paying this debt off."

Mr Patrick said Labor was a chicken and would lose voter support for backing down on integrity issues.

"I had a meeting with a senior Coalition minister last year and what this person said to me is, 'I love playing chicken with the Labor Party because they always swerve'," Mr Patrick said.

Greens senator Nick McKim said the Senate was "not going to insist on a modicum of transparency in regards to the biggest stimulus package in this country's history".

The fracture comes as a private senator's bill led by Senator Gallagher passed and will look to increase transparency about debts waived by the government.