Anthony Albanese will present controversial changes to negative gearing and capital gains tax to parliament on Thursday, pushing for speedy passage of the plans while flagging possible carve-outs for businesses beyond the startup sector.

Labor’s pre-election promise of a $1,000 standard tax deduction will be included in the draft laws, along with the $250 “working Australians tax offset” announced in the budget.

The prime minister wants the “core” elements of the plan through parliament by early July, setting up a challenge for the Coalition and One Nation, who would have to vote against the tax cuts if they choose to oppose the budget measures.

But Labor MPs expect Tuesday’s caucus meeting to include heated debate about the CGT changes amid a backlash from investors and startup founders.

Guardian Australia understands some within Labor are angry the budget message has drifted away from intergenerational fairness in the housing market, and that the government has struggled to explain the benefits of replacing the 50% capital gains tax discount with an inflation-based model.

Giving exemptions to some businesses – such as businesses in their first few years of operation – would “take some heat off”, one MP told Guardian Australia. Others are wary that scare campaigns could “get out of hand” without clearer explanation of the changes from Albanese and the treasurer, Jim Chalmers.

Albanese said rule changes to tax treatment for trusts would come later in the year.

“That’s the normal way that tax policy has been implemented for a long period of time,” he said, outlining ongoing consultation with the tech sector and business groups.

He challenged the opposition leader, Angus Taylor, to support the plan, even as the Coalition regroups through strong opposition to the budget tax changes. Taylor has pledged to repeal the changes if the Coalition wins the next election.

“We will learn on Thursday whether they have learned anything from the last election,” Albanese said on Monday.

Albanese wouldn’t be drawn on whether a Senate inquiry into the changes would be required, with the Greens likely to decide the legislation’s fate. Leader Larissa Waters labelled the changes “tinkering around the edges” and called for about 4 million low-income earners and welfare recipients, whose income is below the tax-free threshold, to receive the next $250 offset.

The government has tried to wrestle the debate back to its preferred territory in recent days, attempting to reorient focus away from the more complicated tax changes.

Asked about a public campaign criticising the effects of the CGT changes on businesses, including billboards at Canberra airport, the housing minister, Clare O’Neil, argued the budget was aimed at housing.

“The main issue that most Australians face in their lives is trying to realise the aspiration to own their own home,” she said.

“Let’s remember here that the budget is about trying to reshape the housing opportunities for Australians and the people that we are thinking about are the millions of people around our country who are struggling right now.”

Independent MP Allegra Spender said that rushing through legislation was the wrong idea, warning of “some very significant unintended consequences” on businesses.

“I think there is a long way to go between the budget announcements and where we need to go,” she said.

The Australian Chamber of Commerce and Industry chief executive, Andrew McKellar, said carve-outs would not be adequate and called for a total overhaul of the government’s plan.

“The government says its priority is lifting our dwindling productivity, but you won’t get business investment if you are going to tax investment; it is counterproductive,” he said.