Julia Gillard has taken a double whammy in the latest poll.

The Prime Minister's approval rating has reached its lowest point, apparently over her carbon tax plan. And she is losing to Kevin Rudd as preferred Labor leader.

Today's Herald-Nielsen poll confirms that the Labor Party remains near its historic low point among voters and would decisively lose an election held today.

But its troubles are compounding as its leader loses standing: Gillard's approval rating is down by 5 percentage points to 47 per cent in a month, her lowest since taking the leadership. With her disapproval rating rising by 4 to 47, her net approval rating is now zero.

"I think the broken promise line is doing the damage," said the Herald's pollster, John Stirton, of Nielsen.

Gillard's consolation? Tony Abbott is also losing personal approval, is also losing to his main rival for his party's leadership, and remains well behind her as preferred prime minister.

"The poll reflects that both party leaders are relatively unpopular following a period where both leaders were relatively popular," Stirton said. "Politics has become a lot more combative in the last 15 months and voters wish for a time when it was less so."

In today's poll, Abbott's approval rating has fallen by 3 percentage points to 43 per cent, while his disapproval is up by 3 to 52. This gives him a net approval rating of minus 9.

This two-party share of the vote appears to be unaffected by the eruption of the debate over Labor's proposed carbon tax. Only the standing of the leaders seems to have been affected.

Julia Gillard's popularity plummeting