Scott Morrison has said he would have difficulty looking his children in the eye if he ceded to a backbench push to water down superannuation reforms designed to limit use of super as a tax minimisation strategy.

In an interview on 2GB radio on Monday, the treasurer confirmed he is having “open conversations behind closed doors” about the reforms but strongly criticised doubling the life-time cap on non-concessional super contributions.

The comment came after reports on Friday he is considering increasing the $500,000 cap proposed in the May budget and taken to the July election.

The outspoken conservative critic of the superannuation reforms MP George Christensen tweeted on Sunday that he wanted the cap doubled from $500,000 to $1m.

A doubling of the proposed lifetime cap would satisfy most concerns over the Coalition superannuation policy. #auspol — George Christensen (@GChristensenMP) August 20, 2016

Asked about increasing the non-concessional super cap to $750,000, Morrison said: “We’re still working through that process with my colleagues.”

He said if amendments were made alternative savings would need to be found “to make up the other $250 to $550m”, for the first time putting a price tag on a mooted back-down.

“This is the process we’re working through. I’m doing that with my colleagues, around the country, we’re sitting down in open conversations, behind closed doors and working this through. I’m not negotiating this through the media – I’m doing this directly with my colleagues.”

Morrison said the proposed backdown would affect people who “want to put $1m after tax into their superannuation so they can pay 15% on it rather than their marginal tax rate” and had already transferred $1.6m to a tax-free account.

“I find it pretty hard to look my kids in the eye and tell them they’ve got to saddle a higher debt because someone who had a very big income wanted to pay less tax.”

On Friday the Australian Financial Review reported Morrison was considering increasing the $500,000 cap on non-concessional super contributions proposed in the May budget to $750,000 or changing the start date of the cap.

When asked to rule out the changes, a spokeswoman for the treasurer said the government was consulting on the “implementation” of the superannuation reforms taken to the election. “The government will consider technical changes to assist in the implementation of these necessary reforms,” she said.

The stoush around the equity of the superannuation system comes as welfare groups wrote to the prime minister and opposition leader on Friday calling on them not to do away with the $1.34bn energy supplement.

The supplement was introduced in 2013 to compensate welfare recipients for the carbon tax. The government proposes to remove the payment through its omnibus savings bill, which it says draws together $6.5bn in savings Labor had said it would enact if elected in July.

The letter said cutting the supplement would cut payments to 2.2 million people on the lowest incomes including pensioners, sole parents, single-income families, carers and Newstart recipients.

It would result in a $4 a week reduction to Newstart, which is already “well below the poverty line”.

The letter was signed by the Australian Council of Social Service, the Australian Youth Affairs Coalition, the Australian Unemployed Workers’ Union, Carers Australia, Jobs Australia, the National Welfare Rights Network, the National Council of Single Mothers and Their Children, People with Disability Australia and the Welfare Rights Centre.

On Friday the shadow treasurer, Chris Bowen, said it was “humiliating” for the treasurer to make changes to the government’s super policy in an effort to calm the Liberal backbench.

“[Morrison] should be on the front foot and tell people, the superannuants of Australia, those who have invested in good faith under existing rules, just what his policy is,” he said.