Labor looks set to rely on the Greens for support for the digital duty of care laws when Communications Minister Anika Wells tables the legislation on Thursday, but will likely face a five-week Senate inquiry ahead of the final sitting period.

Ms Wells and Prime Minister Anthony Albanese have expressed their eagerness to get the legislation through Parliament but have faced criticism and demands from the crossbench and Coalition.

Ms Wells has since revised the Bill from the September exposure draft by axing controversial provisions for ministerial decision-making on “serious harm”, instead handing that responsibility to Parliament.

The Coalition have been vehemently against the initial draft and have actively called for Australia’s to join their petition to “kill the Bill” insisting Labor was “desperate to impose political censorship”.

One Nation leader Pauline Hanson says the laws would impinge on freedom of speech and were designed to target her party.

But the Greens haven’t ruled out supporting the Bill and have demanded tougher regulation, higher fines and a private right of action to allow individuals to sue major tech platforms for harm suffered online.

On Tuesday, Greens members said that while they were still in negotiations and hadn’t seen the final legislation they were committed to send the Bill off to a Senate inquiry.

However, they questioned Labor’s decision to introduce the Bill on Thursday rather than a Wednesday which would only give the Senate hours to consider whether to refer it.

Ms Wells is scheduled to speak about her legislation on Thursday during a National Press Club address titled “A global reckoning: Why Australia needs a Digital Duty of Care”.

“In a perfect world, we would be getting significant reform through before the end of this year,” Greens leader David Shoebridge said.

“This is an important reform, and getting it right, letting the public have a say, giving time for us to consider what I think will be some quite complex negotiations on amendments will be important for the Greens.”

Senator Shoebridge accused the Coalition of choosing “to deal themselves out” of the negotiation because they wanted to “dance to the tune of One Nation” on the Bill.

“They want to sort of dance to the tune of One Nation on this, spreading lies and disinformation about the bill,” he said.

“It’s kind of almost ironic, isn’t it, that there’s out there actively spreading lies and disinformation about a bill that’s trying to hold big tech to account.

“The Coalition choose to deal themselves out of that, that’s a matter for them.”

The laws will cover social media, search engines, AI chat bots, dating apps, gaming and messaging platforms, and pornography sites among other online services and are designed to shift responsibility to platforms.

Tech giants will likely be forced to take down harmful content, conduct regular safety audits, and be transparent about data collection and algorithms.

Labor Senator Murray Watt said Labor wants to see the laws passed as soon as possible on Tuesday, and pointed to concern over Australians’ ability to watch a live stream of a firing squad execution in the US.

The Trump administration has a proposal to ensure the public can watch the scheduled December 3 execution of former US Army major Nidal Malik Hasan, convicted of killing 13 people and injuring dozens more in a shooting at the Fort Hood military base in 2009.

“We want to see these laws passed and even this recent example of this execution and the possible streaming of it is an example that we need to strengthen Australia’s laws as it relates to the responsibilities of the tech platforms,” Mr Watt said.

“We remain open to passing this legislation either with the Coalition or the Greens and I know that Minister Wells is in discussions with both sides about that.

“It’s too important to have this blocked through some sort of politics from either side.

“We will continue discussing with both the Coalition and the Greens.

“But we need to put the interests of Australians first on these sorts of things.”

Greens Senator Sarah Hanson-Young told ABC RN Breakfast that the fines for non-compliant big tech companies should be tied to their global revenue rather than a set figure, which she says would not deter them.

She also welcomed Ms Wells’ decision to remove ministerial discretion powers but wanted more before the Greens would be willing to give the Bill support.

“All the experts around the world say that if you want to hit big tech where it hurts, if you want to hold them accountable and make them pay for the consequences of their harm and damage, that it needs to be a percentage of global revenue,” she said.

She added that responsibility should not be left to the eSafety Commission to hold tech companies to account and Australian individual users should have the ability to act if they are harmed online.

Shadow communications minister Sarah Henderson told a CPAC conference in Brisbane over the weekend that the Bill was “dangerously vague”, “incoherent” and a threat to political speech.

She labelled her Labor counterpart the “minister for Ooshies and travel rorts”, mocking Ms Wells’ social media videos and travel bills.

“Labor’s proposed digital duty of care is dangerous, undemocratic and it must be stopped,” Senator Henderson said.

“Labor is desperate. Desperate to control the narrative. Desperate to silence its critics — the podcasters, the influencers, its political opponents.

“Desperate to impose political censorship, to shut down your voices.”