The New South Wales Liberal premier, Gladys Berejiklian, believes taxes should be looked at when trying to tackle housing affordability, although she says supply remains the key issue.

“I am very open to looking at potential tax changes to improve housing affordability,” Berejiklian told Sky News on Sunday.

The prime minister, Malcolm Turnbull, and the treasurer, Scott Morrison, have both repeatedly dismissed the idea of curbing housing tax concessions, such as negative gearing and capital gains tax.

Making it easier to buy a home will be a key concern for this May’s federal budget, an issue Turnbull has admitted is complex. But he says the key is ensuring there are enough homes available.

“It is essentially a supply and demand problem,” he told reporters in Darwin.

Morrison has raised the threat of increasing taxes more generally in the face of the Senate continually blocking spending cuts, especially the government’s latest omnibus bill, which proposes welfare cuts to help pay for childcare reforms and funding for the National Disability Insurance Scheme.

Failure to curb spending and get the budget back into balance puts the nation’s triple-A rating at risk.

However, Berejiklian is “absolutely confident” the federal government won’t hit health and education funding in efforts to save the rating.

“The federal government will find a way which manages their needs in terms of the triple-A rating, which strengthens their budget position but doesn’t necessarily hurt those core services,” she said.

The premier believes there is room for the states to have more autonomy in raising revenue, saying the present system, which hasn’t changed for decades, leaves them having to rely on more volatile taxes.

She thought it was “regrettable” last year’s GST debate had been and gone with no reform.

The federal government may be making some modest progress in trying to gain support for its 10-year business tax reduction plan.

The Senate powerbroker Nick Xenophon now says he may consider a reduction for firms with more than a $10m turnover, having previously only supported giving tax cuts to small businesses below that level.

“We’ll talk to government about maybe going a step further on that,” he told ABC television. “But to give multibillion-dollar companies tax cuts at this stage, given the alternative appears to be hitting low-income earners, that doesn’t seem fair.”

It was his objection to the omnibus bill, which drew a hostile response from the government and the threat of higher taxes.

Xenophon hopes he can reach some common ground with the social services minister, Christian Porter, once the “the dust and the acrimony” has settled. He said the childcare package was unambiguously a good thing.

But he hit back at the assistant minister to the treasurer, Michael Sukkar, who accused the senator of wanting to impoverish the rest of Australia.

Xenophon said the remarks were “ignorant”, “stupid”, “ ill-informed” and not very helpful.