Malcolm Turnbull could face another challenge to his leadership today.

Peter Dutton supporters have signed a petition overnight, demanding another party room meeting and leadership vote.

But they may struggle to get enough support from MPs to force the meeting to go ahead.

Australian correspondent Murray Olds told Mike Hosking Turnbull could nip it in the bud, and call the meeting himself.

"There's no compulsion on the Prime Minister to do so, but the optics are terrible. He just looks like a dead man walking."

New polling shows Dutton could fare even worse than Turnbull at the next election.

LISTEN TO MURRAY OLDS TALK WITH MIKE HOSKING ABOVE