Barnaby Joyce appears to be haemorrhaging support within his party and the government as speculation mounts he will not survive long enough to serve as Acting Prime Minister when Malcolm Turnbull heads to Washington next week.

Long-serving former National Party leader Warren Truss told the ABC’s 7.30 program his successor, Mr Joyce, had “certainly been diminished” by the scandal of his extramarital affair.

As the interview went to air on Tuesday night, reports were already suggesting a group of Nationals was mustering to force his resignation.

Mr Truss said the leadership “issue” needed to be “resolved and resolved quickly“.

He said Mr Joyce could stay on if he managed to “demonstrate he’s got the capacity to continue to do the job”, but added the Nationals leader had “undoubtedly been diminished”.

Asked if Mr Joyce should quit, Mr Truss said he was “sure that members of Parliament are assessing those issues as we speak”.

That appeared to be the case with widespread reports that a growing number of Nationals MPs were either actively pressuring Mr Joyce to resign or were close to doing so.

As of late Tuesday night, no delegation had been to see Mr Joyce to discuss the leadership, the ABC reported.

Mr Joyce’s two apologies earlier on Tuesday – one in public and another to the Coalition party room – had not appeared to head off the threat to his leadership.

With suggestions rippling through Parliament House that Mr Joyce could be forced to quit, two Nationals MPs were forced to deny the existence of a leadership coup while attending a domestic violence event held at Parliament.

Veterans Affairs Minister Michael McCormack, a Nationals frontbencher who missed out twice on becoming deputy leader, has been touted as a potential leadership successor.

He denied on Tuesday that he had been having conversations with colleagues about replacing Mr Joyce, telling reporters: “No, I haven’t.”

While an unnamed Nationals MP was quoted by the ABC as saying the  scandal surrounding the Deputy PM is “playing very, very poorly in the electorate and is all anyone can talk about”, others feel Mr Joyce remains best qualified to lead the party.

“There is significant concern, but I believe the balance is in Barnaby’s favour,” the MP was quoted as saying.

“We have to look at the attributes of Barnaby in terms of what he can deliver as a Minister for Infrastructure and Transport.”

Since the revelation that Mr Joyce, a married father-of-four, is now expecting a child with former staffer Vikki Campion, a series of damaging stories about government jobs that were handed to his new partner and the use of taxpayers’ money have further dented Mr Joyce’s standing.

On Tuesday, Fairfax Media reported that Mr Joyce had charged the taxpayer to stay in Canberra while Parliament was not sitting on 50 occasions last year, a figure that far exceeded any other government minister.

Mr Joyce’s office said the high figure should be expected because, unlike other capital-city-based ministers, he could not access Commonwealth Parliamentary Offices in Tamworth.

Mr Truss also defended Mr Joyce, saying it “doesn’t strike me as being an exceptionally large amount, bearing in mind the difficulties you have with country air services”.

Victorian Nationals MP Darren Chester, who was unceremoniously dumped by Mr Joyce from the infrastructure portfolio late last year, was one of a number to suggest the ongoing controversy was impacting the government.

“You have to be a mug to suggest this is not a problem for us,” he said.

“When people’s private matters are public knowledge in the way they’ve been aired over the last week, it’s very disturbing.”

Earlier, the Prime Minister, who was also reported to have called Nationals MPs on Tuesday to gauge support for their leader, sought to further distance himself from the controversy.

“The facts of the relationship which you’re referring to are of course known to the Deputy Prime Minister, it is his responsibility to address it and comply with the standards,” Mr Turnbull told Question Time. 

By Tuesday morning, as Mr Joyce delivered his public apology down the barrel of a TV camera, his colleagues had turned their attention to who might replace him.

“I am not predicting anything is going to happen today, but if it does there is going to be a lot of guys with their hands up, and I might be one of those,” Queensland Nationals MP Ken O’Dowd told a local radio station.

Mr O’Dowd later said the remark was a joke.