However, Ms Gillard said her minority government had a lot of ``hard work'' to do to win the next election, with the Nielsen poll giving the Coalition a two-party lead of 53 per cent to Labor's 47 per cent.

Ms Gillard, who on Sunday told a caucus meeting MPs must be more disciplined, brushed off the leadership issue when asked in Canberra about her working relationship with Foreign Minister Kevin Rudd, who is making his way back from security talks in Europe.

``I deal with Kevin Rudd frequently in his capacity as Minister for Foreign Affairs,'' she said yesterday.

``On everything else I will leave you to your fevered speculation - it doesn't need any facts or commentary from me.''

While Ms Gillard overtook Opposition Leader Tony Abbott as preferred prime minister by 48 to 46 per cent, the Neilsen poll published by Fairfax Media yesterday showed Mr Rudd had a 22-point lead over Ms Gillard as preferred Labor leader.

Betting agencies now have Mr Rudd for the first time level pegging with Ms Gillard to be Labor leader by the next election, after weeks of speculation about the leadership ambitions of the former prime minister.

Ms Gillard said she was focused on explaining to voters how Labor was ``reshaping the economy'' for the better.

``We do have a lot of hard work to do, and if we do that hard work I believe we can win the election when it's held in 2013,'' she said.

All of the government's actions and policies should be measured against ``the benefit it brings to the Australian people'', she said.

Greens leader Bob Brown said voters were becoming more supportive of the nation's first female prime minister.

``There's a big swing around from the average punter in favour of Julia Gillard,'' Senator Brown said.

``She is getting a rough time . . . and quite a bit of the criticism is sexist and unfair and unrelenting, and the Prime Minister needs a bit of a break from that.

``The people of Australia are indicating she should have it.''

He repeated the Greens' desire for the Gillard government to serve its full term.

``She may not be the great visionary of political leadership in Australia, but (she's) very strong, very determined, and people are incredibly impressed with her ability to deal with what's been chucked at her. And so am I,'' he said.