Liberal senator Andrew McLachlan has publicly backed Andrew Bragg and urged colleagues to “follow his lead” after a public speech that has split colleagues and triggered a rebuke from opposition leader, Angus Taylor.

At the National Press Club on Wednesday, Bragg announced a policy to slash the national construction code and suggested net overseas migration should be dropped from the current level of about 300,000 to below 180,000 a year to keep pace with new housing builds.

Senior colleagues, including Taylor, were quick to dismiss the migration figure this week, saying they were Bragg’s “personal views” and that the party’s policy was yet to be finalised. The shadow treasurer, Tim Wilson had said: “I don’t think you should bank that at all” in response to the number.

Privately, Taylor counselled his frontbencher.

Moderates, including McLachlan and Queensland senator Paul Scarr, called Bragg’s speech “terrific” while others privately said the reaction by the media and some internally was “overblown”.

McLachlan, an outspoken South Australian senator who has publicly criticised his party’s positions on migration and the climate crisis, said Bragg “delivered a masterclass in thought leadership”.

“His address was an important step in the development of a policy suite that seeks advance the nation,” McLachlan told Guardian Australia.

“His aspiration for Australia is admirable. Every member of the Coalition should follow his lead and discuss policy pathways openly.”

Scarr, who has also defied his party and crossed the Senate floor in March to censure Pauline Hanson after she wore a burqa in the Upper House, said he “thought it was a terrific speech. High-level and reinforcing our core Liberal values”.

Other Liberals have been frustrated at the intervention by Bragg, with one MP saying privately colleagues were angry at the lack of discipline and this could be “his last chance”.

Even after critical commentary from his colleagues in recent days, Bragg has maintained it was important to talk about big ideas.

The NSW senator said while many of his ideas, such as a specific net overseas migration target, hadn’t been green-ticked by the shadow cabinet, it was important to “move the debate on”.

Bragg said voters needed “ambitious policy for tomorrow, not micro-announcements for today that aim to please and appease”.

“I’m confident that we will be rewarded for putting more detail on the table,” he told Guardian Australia.

On Friday, he also corrected comments made in an interview on RN Breakfast where he responded “yes, definitely”, when asked whether Australians should accept substandard homes under his changes to the construction code, which would make energy efficiency standards voluntary.

In a social media post, Bragg said he had misheard the question, adding “houses built to this standard would be strong, safe and sound homes with all the basic amenity, such as insulation, plumbing, sewerage etc”.

“I did not intend to agree that houses complying with the Basic Australian Standard would be ‘substandard’. They wouldn’t be.”

One Liberal MP, who spoke on the condition of anonymity, said there had been overreaction to the speech internally which likely came from “not reading what was actually in the speech”.

“Like any disruption, you might be a bit uncomfortable first. I think maybe just a little bit of surprise for some. I think he did a good job and he was brave.”

They welcomed the fresh take from Bragg and said the Sydney senator consistently showed he wasn’t a “benchwarmer”, but wanted to engage in substantial policy.

“Clearly what we’ve been doing over the last five or six years in particular has not worked. So maybe taking a different approach or approaching the problem in a different way is a sensible thing to do.”

The Nationals leader, Matt Canavan, was quick to shoot down any cuts to working holiday visas as Bragg suggested in his speech, but praised his “big ideas”.

“I love Andrew Bragg. He’s he’s full of ideas … we need people like him because he’s full of energy and enthusiasm,” he told ABC’s Radio National on Friday.