Green Party co-leader Metiria Turei says assumptions she could have drawn on family support instead of lying to Work and Income are wrong.

Ms Turei has hit out at opponents outside the party, saying they are using her story to try to bring it down, after the party reached a compromise with two dissenting MPs.

Kennedy Graham and David Clendon yesterday withdrew from the party's caucus, saying they objected to her stance on benefit fraud.

Mrs Turei has admitted lying to Work and Income as a solo mother in the 1990s and, while acknowledging what she did was wrong, has refused to condemn others forced into the same position.

Yesterday, she struck back at "wild accusations" she had faced by opponents since making what she did public.

"They want to see us fail at the election and they're using me as a target."

She told Morning Report the questions she was facing about her circumstances at the time - including the fact she lived with her mother - were the same type of questions thousands of beneficiaries were asked by Work and Income.

"What we're seeing is what it's like for a beneficiary to have to justify their lives... We're just seeing it play out in public."

There was an assumption that her mother was taking care of her financially when they lived together, Mrs Turei said.

"My mum was sick for quite a lot of the time and so we lived together in order to be able to ... both be as best as we could and as well as we could."

She also took exception to suggestions she could have relied on her partner's mother, Ann Hartley, a successful real estate agent who went on to become an MP and North Shore mayor.

"I drew on as many of the resources that I could, as people do.

"I've also been really clear about the support that my family - my broad family - have provided me ... and I'm very grateful to them for that, but that doesn't make living on a benefit easy or even possible."

Work and Income's rules meant accepting money from family or even food was considered additional income that could affect someone's benefit, Mrs Turei said.

"It's not as simple as saying, you can go around getting resources from other people."

She conceded she could have paid back what she owed Work and Income many years ago but had not.

"I could have made that decision and I didn't and these are the consequences of that."

Mrs Turei said she had been taken aback by Dr Graham and Mr Clendon's reaction to her revelations.

"I sent them a draft copy of the speech [in which they were made] but I hadn't had any response from them," she said.

"The first that I heard from Kennedy was the evening of the Sunday when I gave the speech.

"They didn't tell me beforehand that they had serious or principled concerns - and I wish they had."