Andrew Bolt has raised the prospect of Cory Bernardi emerging as the head of a new political party that would sit significantly to the right of Malcolm Turnbull's Liberals and their National Party colleagues.

Appearing on The Project, conservative columnist and commentator Bolt was asked by regular panellist Steve Price if Australia's freshly minted 29th Prime Minister, widely seen as far more liberal in his views than his immediate predecessor, would be able to win the trust of conservatives.

Liberal senator Cory Bernardi. Credit:Alex Ellinghausen

Bolt replied that in the wake of Turnbull's challenge and subsequent win on Monday, he had received 1000 comments and emails from readers, "of which 99 per cent are red hot, 'I'll never vote Liberal again'.

"You've had the same on the radio show," he added to Price, who is host of the night-time show on talk radio station 2GB. "But … where are they going to go?