Opposition NDIS spokeswoman Melissa McIntosh dug in on her comments made on Monday, urging for the Liberal Party to be overhauled.
A number of her colleagues dismissed the suggestion, while Labor used the divergence to attack the opposition as divided.
Acknowledging she had been blunt, Ms McIntosh said she wanted to see her party's policies resonate with voters.
"We are pretty much the heartland of Australia," she told Nine's Today program on Tuesday.
"When the heartland of Australia tells you that you need to get more cut-through to get more voters on your side, then you need to listen to the people."
Addressing the joint party room on Tuesday, Angus Taylor reinforced the importance of the coalition being "very disciplined" in taking that message back to voters particularly over the five-week winter break.
Deputy leader Jane Hume also backed in that message, telling her party "we must be relentlessly disciplined" and talk about the issues affecting voters.
Frontbencher Michaelia Cash said there was a while to go until the next federal election and an overhaul was not needed.
"Australians don't want us to rebrand, they want us to change the country that is actually going backwards under Larissa Waters, the Australian Greens, and Anthony Albanese," she told Nine's Today.
Opposition foreign affairs spokesman Ted O'Brien said he was not proposing a rebrand of the party.
"We do need to communicate more with the Australian public about the fact that it's only the Liberal Party that will look after Australian families," he said.
"We just have to keep on those messages."
During a particularly rowdy Question Time, Liberal MP Garth Hamilton was suspended from parliament for 24 hours after swearing and storming out of the chamber.
Responding to a Labor attack on comments Mr Taylor had made about bushfire management, Mr Hamilton - a former volunteer firefighter - slammed his desk drawer shut and shouted "f***ing bullshit".
Speaker Milton Dick described the incident as a "new low", but Mr Hamilton was unrepentant and said the government's attacks on Mr Taylor were "gutter politics".
As Pauline Hanson's party has surged in popularity, at one point polling higher than Labor, the coalition has not ruled out a potential preferencing deal in elections.
But a more recent poll shows that following the One Nation leader's first National Press Club address earlier in June, her personal approval ratings have dipped.
Mr Taylor has failed to reverse dire polling after ousting Sussan Ley in February, with the coalition's primary vote dropping to a record low of 17 per cent in the latest Newspoll.
Labor sits at 33 per cent, while One Nation follows at 29 per cent.
Greens senator Sarah Hanson-Young said the Liberal Party had already been rebranded.
"It's done. It's called One Nation," she told reporters.
