Major business groups have urged Labor to suspend its immigration changes and consult further with industry about how to get more skilled workers into the country, amid questions about looming Labor tweaks on permanent migration.

With home affairs minister Tony Burke delaying an anticipated immigration speech by at least one week, some Labor MPs say they are anxious to avoid major changes to the family and humanitarian visa categories, with one urging against “performative reductions” in migration in response to One Nation.

But other Labor sources characterised Burke’s as tweaks to existing settings, with an expected focus on enforcement of existing rules and small pruning of various programs.

“Tony’s doing an absolutely fantastic job of ensuring, that our immigration program which is so vital for us economically, vital for our vibrancy … the world’s most successful multicultural nation. But it must be properly calibrated,” said energy minister Chris Bowen.

Burke was to deliver a National Press Club address on Thursday about migration policy, but withdrew on Tuesday with a spokesperson telling media “some elements of the speech would not be finalised” in time.

The ABC reported measures could include tougher family visa rules, capping backpacker numbers, or restrictions on asylum seekers. Burke’s office would not confirm media reports, and senior sources in the government remained tight-lipped on the changes.

Some sources said they believed media and stakeholder focus on Burke’s speech had been overegged, characterising the changes as more “surgical” adjustments across multiple migration areas, and downplaying major changes to work, family or humanitarian visas.

Another Labor source said they expected Burke’s speech would focus on how Labor plans to cut permanent migration to 185,000 per year – a target the government has cited in budget papers – rather than any cuts below that number.

That figure includes about 132,000 skilled migration places and 52,000 partner and family visas.

But potential cuts to either stream are already facing pushback from business groups and government members.

Outside what will be detailed in Burke’s speech, his department recently announced that skilled migrants who are already in Australia would be given priority for permanent residency, which could help lower total migrant numbers, but also decrease the pipeline of available workers.

The Minerals Council of Australia called on the government to “suspend skilled migration changes and consult industry” more closely on those changes.

MCA’s CEO Tania Constable said the reforms would “make it harder for mining and other sectors”, raising fears about skills shortages and risks to project timelines, earnings and the economy. She said mining companies were already struggling to find workers.

“Demand from these sectors for specialised skills is already growing faster than migration pathways can adapt, and industry is frustrated and impeded by slow updates, credential barriers and settlement constraints,” Constable said.

Acting prime minister Richard Marles denied rumours of a disagreement with Burke in a cabinet meeting on Monday.

“Migration obviously plays a really significant part in our economy, but it needs to happen at a sustainable rate,” he said.

Pauline Hanson told News 24 that she didn’t care if employers groups thought a migrant crackdown “is going to affect their businesses.”

“I don’t care. My concern is for those Australians that can’t get a roof over their head,” she said.

Labor MP Jerome Laxale told the ABC that Labor would strive to meet its 185,000 permanent migration target.

“If that requires tweaks to our policy to do so, we just have to do that,” he said.

Australian Chamber of Commerce and Industry CEO Andrew McKellar said it would be a “concern” if Labor was to trim working holidaymakers, while cutting family visas would also be a disincentive to attracting skilled workers.

“The government should proceed with caution, we don’t want to shoot ourselves in the foot,” he said.

“It would have a damaging impact if the government was to try to curtail those categories in a draconian way.”

Master Builders Australia CEO Denita Wawn added the datacentres boom would need a new boost to construction workers, calling for tradespeople to be prioritised.

“Migrant tradies ultimately contribute to far more homes than they consume, especially when they reside here over the long term,” Wawn said.

Guardian Australia also spoke to several Labor MPs who said the government should tread carefully around partner visas, warning any cut to family categories would raise anxiety across communities.

One MP said everyone including the government should stop being “hysterical” about migration numbers, and wanted to see firmer pushback by Labor against One Nation’s immigration rhetoric.

“I am against performative reductions, I am in favour of steady migration … Getting skilled people in from overseas is imperative,” they said.

“[Burke is] possibly driven by desire to be seen to be reducing migration rather than anything of substance.”

Another MP said they would be concerned if the government reduced Australia’s humanitarian intake, while a third said cutting backpackers could be a way forward.

One MP said there was confusion among those outside the cabinet who had not yet been advised of any changes. All said the issue was complex, and while reform across the system was needed, that the messaging critical – especially amid the rise of Hanson and One Nation’s anti-immigration agenda raising fears in migrant communities.