Prime Minister Tony Abbott has insisted that he will remain leader of his party and the nation in a tense interview on Melbourne radio.

In a thinly-veiled swipe at party room colleagues, Mr Abbott said: “You do not change leaders, you rally behind someone and stick to the plan.”

He dismissed as “nonsense, absolute nonsense” the speculation that he may be ousted before the next federal election because he is so unpopular.

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Mr Abbott faced a number of angry talkback callers on 3AW on Thursday, one of whom described him as being “on the nose” with Liberal voters.

“You’re the world’s worst salesman,” said the self-declared Liberal voter.

Mr Abbott said his government had a solid record, and tried to blame his failure to pass many key pieces of legislation on “difficulties” with the Senate.

He suggested that boasting more often of his successes might help.

“I could be a bigger and more effective skite sometimes.”

Government backbenchers are growing increasingly frustrated with their leader, according to media reports.

The ABC reports that it has canvassed more than 20 per cent of the Coalition across five states and found that most want Abbott to lift his game but only a few want him replaced.

An unnamed Liberal politician quoted in the Sydney Morning Herald described the government as being in “anarchy”, which he or she attributed to the “command and control” exerted by the PM’s office.

The Prime Minister has “lost of the respect” of his colleagues and has “just months” to turn around his performance, a senior Liberal was reported to have said.

Mr Abbott described the story as “nonsense”, but did not directly challenge the veracity of the quotes.

Government leader in the Senate Eric Abetz was forced to respond to questions about the party leadership during a press conference in Tasmania late on Thursday morning.

Senator Abetz admitted that there may be “one or two” grumbling backbenchers, but insisted the overwhelming majority were committed to the government’s agenda.

The Senator also seemed to cast doubt on the so-called “senior” Liberal who put an expiry date on Abbott’s leadership.

“What’s the name?” he said. “Ah, see, there’s no name.”

“If this sort of backgrounding is occurring, it’s just people who are not willing to put their names to it.”

The latest polls show Labor in an election-winning lead and give Mr Abbott a majority disapproval rating.

The Prime Minister tried to reset his political message early in the new year after extensive backlash to the government’s first budget and its poor management of the national debate on such topics as health, education and taxation reform.

This plan almost immediately backfired when the government’s stealthy attempt to implement a GP co-payment via a legislative backdoor was widely criticised.

Mr Abbott was forced to instruct his health minister to reverse the changes. There are also reports of a verbal stoush between Treasurer Joe Hockey and the embattled leader over the co-payment attempt.

A Morgan phone poll taken last week rated Mr Abbott third behind Malcolm Turnbull and Julie Bishop as preferred Liberal leader.

—with AAP