The furore over the elevation of Liberal rogue turned independent MP Peter Slipper to Speaker of the House of Representatives continues to boil.

On Thursday the Opposition claimed Labor was trashing the Westminster system by appointing a non-Labor Speaker.

But the Government has taken a swipe at Opposition Leader Tony Abbott, saying he is acting hypocritically after allegedly offering the job to independent MP Rob Oakeshott.

Mr Slipper replaced Labor MP Harry Jenkins against the wishes of his former party, whose members have taken to dubbing him "a rat".

The move gives the Government a two-vote majority on the floor of the Lower House.

Leader of the House Anthony Albanese says Mr Abbott made an offer to Mr Oakeshott on Thursday morning.

"I noticed Tony Abbott saying this morning that he wouldn't have done something like this," Mr Albanese said.

"Well, Tony Abbott and his team spent all of yesterday morning trying to coax an independent, any independent would have done, to stand for the position of Speaker on the floor of the House of Representatives."

Liberal frontbencher Joe Hockey says that is not true.

"Tony Abbott didn't ring Rob Oakeshott yesterday asking him. Not at all," he said.

But Mr Oakeshott says otherwise.

"It's a matter for Joe to look himself in the mirror and ask himself why he's making that up," Mr Oakeshott said.

"About 12:15pm yesterday Mr Abbott rang my office. I accepted the call. He made an offer and I thanked him and rejected it.

"That's the facts. It's up to Joe to try and spin it otherwise, and I guess it's up to the Australian community to decide who they want to believe."

Mr Abbott's office insists Mr Oakeshott approached the Opposition and that Mr Abbott called him and told him directly the Coalition would not be nominating him.

But Mr Oakeshott says at no time did he approach anyone about seeking the speakership.

He released a statement saying Deputy Opposition Leader Julie Bishop, as well as some crossbench MPs, approached him about seeking the speakership.

Ms Bishop says the discussions centred around whether Mr Oakeshott could muster enough support from the other independents to get nominated and that he asked Mr Abbott to call him.

'Good guy'

Audio: Fever pitch furore over new Speaker (PM)

While Coalition MPs rail against their erstwhile colleague, Chief Government Whip Joel Fitzgibbon has nothing but praise for the new Speaker.

"Peter Slipper is a good guy. He's proven to be a competent person in the chair," he said.

Mr Fitzgibbon says the Coalition has itself to blame because it drove the MP to jump ship.

"Peter Slipper was certainly pushed by his own party and those who were out to take his seat, so they created this dynamic for themselves," he said.

"You didn't have to be rocket scientist to work out that if an opportunity presented itself Peter Slipper would take it.

"He's a survivor and my view is he'll continue to survive."

Controversy magnet

Video: Labor's political plays discussed (Lateline)

The Speaker's electoral neighbour, long-time Liberal Alex Somlyay, says Mr Slipper repeatedly attracts controversy.

"We dread opening the local newspaper because of the controversies that he manages to get himself involved in," he said.

"There are a lot of things that we have disagreed on in the past and a lot of those things concern expenditure of public money.

"Peter was always the highest, the big spender in the Parliament, and of course that brought us a lot of bad publicity."

Locals sent a petition to Parliament in September calling for a full audit of Mr Slipper's travel entitlement claims during the past decade.

Mr Abbott says Mr Slipper is now the Government's problem.

"Peter Slipper is the Prime Minister's Speaker and all questions about Mr Slipper, his travels, his use of entitlements, his conduct, should go to the Prime Minister," he said.

Coalition accused of Speaker job hypocrisy - ABC News (Australian Broadcasting Corporation)