The Liberal leader, who toppled Sussan Ley in a spill on Friday, spent his first days in the role outlining key policy battles, including a renewed focus on immigration and economic management.
Conservative Liberals Jacinta Nampijinpa Price, Sarah Henderson and Andrew Hastie are among those expected to make a return to the front bench after resigning or being sidelined from senior positions by Ms Ley.
Senator Nampijinpa Price used a podcast appearance to lobby for a greater role in Mr Taylor's team, claiming she had previously been thrown under the bus by her colleagues.
"I'm back baby, I'm back" she told the Karl Stefanovic Show podcast.
"I was having a breather, but I'm back. The fire's back."
But the firebrand senator refused to apologise for claiming Labor was bringing in Indian migrants because they'd vote for the party - controversial remarks that partly led to Ms Ley dumping her from the front bench.
The first poll released since Ms Ley was ousted shows a small uptick in support under Mr Taylor's leadership.
Asked where their vote would sit under both Mr Taylor and Ms Ley, support for the coalition was three percentage points higher under the new leader than his predecessor.
Under Mr Taylor, 23 per cent of voters said they'd put the coalition first on their ballot paper - a tie with Pauline Hanson's One Nation.
The Resolve survey, published in the Nine papers, was conducted in the final days of Ms Ley's leadership and the first days of Mr Taylor's.
One Nation recorded primary support of 27 per cent in the latest Newspoll, conducted before the leadership change, with the coalition on 18 per cent.
The new opposition leader has also written to Prime Minister Anthony Albanese, calling for a joint audit of government spending run by Labor and the coalition.
"Record levels of government expenditure are contributing to higher inflation, upward pressure on interest rates and a growing public debt burden that will ultimately fall on future generations of Australians," Mr Taylor wrote.
Treasurer Jim Chalmers blasted the demand for an inquiry as a predictable stunt.
"Angus Taylor is the architect of the Liberal party's policy for higher taxes on workers, bigger deficits and more debt," he told Nine's Today program on Monday.
"He is precisely the last person that anybody should be taking lectures from or advice from when it comes to the state of the budget."
Mr Taylor has indicated a more hardline approach to immigration, signalling a focus on protecting Australia's "way of life", likely through some form of tougher vetting of prospective migrants.
"That means shutting the door... on people who are the wrong people who come to this country, who don't accept our basic beliefs," he told Today.
Former senior immigration official Abul Rizvi said Mr Taylor's pointed tough-on-immigration stance appeared to be directly influenced by One Nation's rise.
"He reads the polls as closely as anybody," Mr Rizvi told AAP.
However, he noted strong character requirements already existed for migrants looking to enter Australia, and these had been tightened by anti-hate crime laws introduced after the Bondi terror attack.
Labor had also tightened the previous coalition government's policies on student and working holiday visas that drove a big increase in migration to Australia in 2022-23, Mr Rizvi said.
"Mr Taylor may have forgotten his government also introduced fee-free student visa applications and fee-free working holiday maker applications," he said.Â
"The Labor government were slow to reverse those policies, but they did get rid of them."
Mr Taylor and deputy Jane Hume also vowed to offer lower taxes, a renewed focus on housing affordability and the end of an "ideological approach" to energy policies.
26°C