Peter Dutton has held firm on the government’s line that it needs to continue to push its company tax cut policy through the Senate in the face of a tongue-lashing from the conservative commentator and ally Ray Hadley.

The Sydney radio 2GB host, who has already banned Malcolm Turnbull and Scott Morrison from his program after on-air falling-outs, accused Dutton of being hamstrung by his cabinet position and unable to say “what you really think”.

Morrison, the treasurer, and the finance minister, Mathias Cormann, who handles the government’s negotiations in the Senate, have both maintained cutting company taxes from 30% to 25% over a decade remains government policy, despite a sceptical crossbench and the results of the super Saturday byelections.

“Why are we still pursing it?” Hadley asked during his regular chat with Dutton.

Dutton responded: “Well, the biggest issue, again we need to call this out, the biggest issue out in Longman was the involvement of the unions, lies by Bill Shorten about health funding and the involvement of GetUp. And this hasn’t been spoken much about, but GetUp had a big presence up there. They are making all of these sneaky phone calls scaring people. They are basically a front for the Greens and they received over $1m from the CFMEU and they are targeting seats and they are having an impact. That is the reality.”

Dutton holds a seat neighbouring Longman that GetUp is targeting publicly.

“Look Peter, I know you are in cabinet,” Hadley said. “Barnaby Joyce yesterday, no longer in cabinet, came out and said what he used to say. I am sure if you weren’t shackled by cabinet you would be saying the same thing. Barnaby said yesterday: ‘Look, power, let’s worry about power, that is what people are worried about. Let’s forget about all this other nonsense, let’s worry about that. Let’s worry about the drought, let’s worry about fixing farmers up, let’s worry about that.’

“At the end of the day, this nonsense proposed by the prime … You have just spoken about GetUp and how much money they are spending and making sure that Labor wins elections, as they will no doubt do, but the only thing the prime minister and treasurer have spoken about since Saturday’s shellacking [is], ‘We are standing firm on these tax cuts for big business.’

“Is there a void between the two? Do they have any grey matter between the four sets, or the four ears there, to understand they have got to start talking to the electorate about things that matter? And big business tax cuts are not one of them.”

Dutton maintained the government’s corporate tax cuts proposal was sound policy.

Tony Abbott led the charge on calling for the government to dump the policy if it did not pass the Senate. He was backed by Luke Howarth, whose seat of Petrie neighbours Longman and shares a similar constituency. So far, senior members of the government have held firm with the message to wait and see.

Within a nervous backbench, the tax cuts, which formed the basis of Labor’s byelection message – in a vote in which the Queensland LNP candidate lost almost 10% of his primary vote – are increasingly being viewed as electoral poison.

Labor crafted its message about spending money on health and education, rather than “a tax cut for big business and the big banks”.

With less than a year until the next election, Turnbull and Morrison are facing unease from within the party room, as skittish MPs look for a way to neutralise Labor’s message.

Tax cuts are not the only issue dividing the Liberal party room. The government is also fighting off continued unrest over its national energy guarantee policy, which will be taken to the states next week.