Tasmanian MP Bridget Archer said the coalition needed to come to the table and put forward changes to the emissions reduction measures, rather than oppose them outright.
The government is still negotiating with the Greens to pass the safeguard, which would apply to the country's 215 biggest emitters, but the coalition has indicated it would not back the plan.
Ms Archer said it was incumbent on MPs to make changes to the safeguard for the benefit of their communities.
"I'm utterly exasperated by the lack of engagement from my own side to come to the table and engage in a constructive conversation about how the safeguard mechanism could be improved," she told parliament on Wednesday.
"We should not just support or oppose it for political purposes, but instead seek to adjust the legislation to get the best outcomes for our communities in the country.
"All parties should be engaging in good faith, which has not occurred on this critical piece of legislation."
While she did not state her final stance on the bill, she said she would carefully consider her position once amendments were made.
"I am hopeful that at the very least my comments made here today will encourage greater debate and collaboration from all parties in the Senate with subsequent amendments that may result in a better outcome for business, for the climate and for our future," she said.
The government is aiming to pass the safeguard bill through parliament by the end of the sitting fortnight to ensure it is in place by July.
Labor needs the support of the Greens and at least two crossbenchers for the safeguard to pass the Senate.
Treasurer Jim Chalmers told parliament the bill had the support of the business community and investors, while the coalition was standing in the way.
"Australians and their economy cannot afford another decade of this parliament stumbling and stuffing around when it comes to climate change and energy policy," he said.
Greens leader Adam Bandt said there was still time to get the details of the mechanism right.
"Taking action on climate means dealing with the question of coal and gas. Not just saying it can all be offset but actually ensuring that pollution in this country does not go up," he said.
"We are prepared to work with the government to develop a scheme that actually sees pollution go down."
Greens environment spokeswoman Sarah Hanson-Young said negotiations were still happening in good faith.
"We are determined to get the best outcome for the climate, the best outcome through the parliament that reduces pollution. That's what we're here to do," she told reporters in Canberra.
The opposition sought to disrupt debate on the mechanism in the lower house on Wednesday by moving multiple motions in an attempt to stop government MPs from speaking.
Labor backbencher Sam Rae said the opposition was carrying on "like petulant pork chops" but the government was determined to pass the legislation.
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