Under fire on the ABC's Q&A program from Geoff Thomas, a Vietnam veteran who has a gay son, the Prime Minister – who has allowed her party a conscience vote on the issue – said, however, a "large number" of ALP MPs will not vote the same way as her when the issue comes before parliament

"It's not for me to tell my Labor colleagues or anyone else what they should believe and how they should vote."

Ms Gillard, who lives with her partner, Tim Mathieson, said her views were genuine and that two people could have a relationship of love, commitment and understanding without a marriage certificate.

Mr Thomas, who tackled Tony Abbott on the same program almost two years ago, said that Ms Gillard stood "side by side" with Mr Abbott and "the extremist group" the Australian Christian Lobby.

In a broad-ranging show, Ms Gillard attributed her government's parlous state in the polls to the "heavy lifting" it had done in controversial policy areas such as the price on carbon. She said the "noise and fear" about the carbon price would begin to fade after July 1, when it was introduced.

But she cautioned it would not happen overnight, a sign to the backbench that the polls, too, would not improve suddenly.

"It's very controversial, it's hard, but it's the right thing to do," she said.

Ms Gillard defiantly pushed back at questions implying her leadership was in strife, challenging the host, Tony Jones, to make a date for her to appear on the program during the election campaign in the spring of next year.

Facing an initial barrage of questions on the carbon tax and Kevin Rudd, Ms Gillard said the party had made up its mind on the leadership at an internal ballot on the issue in February.

She also made no apology for the carpet bombing of Mr Rudd by her supporters, from senior ministers down.

"We had a leadership contest. It was resolved at the start of this year. Colleagues told the truth from their perspective," she said of the tumultuous events. "It's done, it's finished, people made their contributions."

Ms Gillard accepted that despite the strong state of the Australian economy her government was unpopular, and attributed that to the contentious policy issues with which it had dealt.

"We have done a lot of really heavy lifting in the first two years of government. It has been, politically, very difficult days," she said.