Liberal backbencher John Alexander will have to fight for his political future on two fronts, after Australian Conservatives leader Cory Bernardi announced he would run a candidate in the Bennelong by-election.

Key points: Mr Alexander resigned because he was "most likely" a dual citizen

Mr Alexander resigned because he was "most likely" a dual citizen Opinion polls show he faces a major challenge to hold Bennelong

Opinion polls show he faces a major challenge to hold Bennelong Losing the seat would threaten the Turnbull Government's slender majority

Mr Alexander, facing a challenge from former New South Wales premier Kristina Keneally, put up to run against him by Labor this week, won the seat on a 19 per cent margin in 2016.

However, two polls showed his two-party preferred buffer had evaporated.

Liberal Labor Galaxy Research 50 50 ReachTEL 53 47

Mr Alexander resigned from Federal Parliament earlier this month after conceding he was "most likely" a dual citizen by descent, because his father was born in the UK.

He had held Bennelong since 2010.

Speaking at the Australian Christian Lobby national conference in Sydney, Senator Bernardi said people needed to support candidates who would "change politics".

He told the ABC he would announce his candidate on Tuesday.

"People are craving a principled and credible alternative to the major parties," he said.

Bennelong was firming up into a tight race between Ms Keneally (L) and Mr Alexander (C), before Senator Bernardi (R) entered the frame. ( Pictures: ABC News / AAP )

ABC election analyst Antony Green said swings in by-elections could be significantly higher.

"As a rule of thumb, they can be twice as large," he said.

Keneally says she'll 'fight hard'

Ms Keneally said about 100 volunteers were door-knocking in the electorate on Saturday.

"I am energised by this campaign, I am in for the long haul in Bennelong," she said.

"We are going to fight hard in this campaign. I am a fighter, and I am standing up, fighting for my local community."

Former prime minister John Howard held the seat for more than three decades before he was rolled by Labor's Maxine McKew at the 2007 election.

"It's a big challenge to be only the second Labor member of Bennelong in the seat's history," said Ms Keneally.

Mr Alexander, who did not have any media events scheduled on Saturday, was also campaigning in the electorate.