Earlier this year, in a bid to reassure international investors, Burnham promised to stick to the government’s existing rules on borrowing.
In his speech, Streeting also contested Burnham’s argument that the north of England had suffered from 40 years of “neoliberalism”.
“It’s more complicated than that,” he said, adding: “We’ve been through several waves of change that have delivered genuine strengths, but also deep weaknesses.”
Such was his emphasis on fiscal discipline – he cited former chancellors Gordon Brown and Nigel Lawson – some in the room mused whether he was making a subtle subsidiary pitch to be chancellor if he was the runner-up in a leadership race.
But he insisted he could win the top job by convincing Labour members that he could win a general election, and unite the centre with the left.
If he did become prime minister, he said he would rule out an early election and govern for the remainder of the parliamentary term.
Elsewhere, the Ilford North MP said that he wanted to see tax on employment come down when “the public finances allow” and repeated his call for capital gains tax to be equalised with income tax rates.
Asked if he would consider getting rid of the triple lock on pensions in order to pay for defence, Streeting said the measure, which guarantees certain rises in the state pension, was “here to stay for the entirety of this Parliament”.
In a jibe at another Labour colleague, Streeting suggested Energy Secretary Ed Miliband should approve North Sea oil and gas drilling projects in Rosebank and Jackdaw.
“There is a pragmatic case for producing our own gas rather than importing from abroad,” he said.
When in opposition, Miliband had described a licence issued to Rosebank as “climate vandalism”.
A full list of the candidates standing in the Makerfield by-election can be found here.