Treasurer Jim Chalmers has rejected claims he and Prime Minister Anthony Albanese are at odds over the significant backlash to the budget.

The Treasurer was forced to back down on elements of his changes to capital gains tax concessions and family trusts after outrage from the business sector.

But after the pair hosted a press conference together to announce the refined changes, the Treasurer was asked whether the relationship had turned sour.

Grilled at a press conference on Friday if Mr Albanese and Mr Chalmers’ relationship was “frosty”, Mr Chalmers said: “It’s just rubbish”.

“You shouldn’t believe that sort of trash that you read in some parts of the media. I talk to the Prime Minister almost every day since the Budget.

“We work together very, very closely on a personal level. I’m very grateful to him for the work that we are doing together to bed down these really important changes.”

Mr Chalmers said he and the Prime Minister knew the tax changes were “politically difficult” but would rather navigate the issue than let young Australians remain “locked out” of housing.

“These changes are more important than the political commentary and the week-to-week polls, because at the end of the day this is really about making it easier for people to buy a home.”

But the budget backlash has reignited rumours that Mr Albanese may retire before the next election.

Shadow treasurer Tim Wilson said both the Prime Minister and Treasurer would “fall” before the election due in 2028.

Appearing alongside Health Minister Mark Butler on Seven’s Sunrise, Mr Wilson suggested it was his fellow panellist who would take up the top job.

“The person who’s going to win out of that is going to be Prime Minister Mark Butler,” Mr Wilson said.

Mr Wilson said the Treasurer had “hashed it up so badly” that Mr Albanese was left with no choice but to “get rid” of Mr Chalmers.

“But that will probably be the Prime Minister’s demise, and the person who’s going to be the beneficiary is going to be the person on your program right now, Mark Butler,” he said.

Mr Butler, who has previously been asked to rule out higher ambitions, called it “total rubbish”.

The Health Minister also shot down the suggestion that Mr Chalmers and Mr Albanese were at loggerheads.

“This is an enormously productive relationship, which I watch up close,” Mr Butler said.

Speaking to Sky News in April, Mr Butler refused to rule out the possibility of replacing Mr Albanese. 

“I’ve supported Anthony, probably more closely and more consistently than anyone else in the caucus,” Mr Butler said.

“I don’t want him to go anywhere. I feel privileged to be able to serve under him and I think I’ve got the best job in the government supporting Australians’ needs in health.”

Albanese throws Chalmers under the bus in brutal budget retreat

However, pressed on whether he had any desires to succeed Mr Albanese, the Health Minister did not rule it out.

“It’s just not something we’re thinking about. I mean, Anthony, I think, said last week, he’s enjoying the job,” Mr Butler said.

“It’s a hard job, but I think right across government, we want him to stay in it for the long term.”

Mr Albanese was asked by Sky News Political Editor Andrew Clennell if he would definitely run again in 2028.

“Of course,” the Prime Minister responded during a Q&A session at the Australia’s Economic Outlook event earlier in June.