Tony Abbott has called on the Senate to do the “right thing” and vote to scrap the carbon and mining taxes, saying December is the time to deal with “unfinished business”.

The prime minister and Opposition Leader Bill Shorten will on Monday fly to South Africa for Nelson Mandela’s memorial service, missing most of the final week of parliament.

But with the government staring at defeat on its push to scrap both the mining and carbon taxes, Mr Abbott posted a message on YouTube directed at Australian voters and the Senate.

“December is the time to deal with unfinished business – and to clear the decks for a good start to the new year,” he said in Sunday night’s message.

“At the election, you voted to scrap Labor’s carbon and mining taxes.

“So, I call on the Senate to do the right thing this week and to scrap Labor’s bad taxes to give our economy the clean start it needs for 2014.”

Mr Abbott said axing the carbon tax would save Australian families hundreds of dollars a year, while scrapping the mining tax would boost job security.

In spite of the appeal, the coalition is likely to suffer mixed fortunes on its legislation this week.

The Greens have thrown the coalition a lifeline on the debt ceiling, with changes expected to be passed by the Senate on Monday.

However, it’s almost certain the stoush over the carbon and mining taxes won’t be resolved, regardless of Mr Abbott’s threats to keep parliament open until Christmas.

Shadow treasurer Chris Bowen said Labor’s opposition to the tax repeals was not motivated by revenge.

Labor was not being obstructive because of Mr Abbott’s own obstructionism in opposition, he said.

“We’ll call it as we see it, and we’ll call it on its merits,” Mr Bowen told Sky News on Sunday.

“It’s not revenge. It’s staying true to our values.

“When people vote Labor, they expect us to stay true to our values, and we’ll be doing that.”

Environment Minister Greg Hunt demanded Labor back the government’s carbon tax legislation, saying: “We don’t want delays. We don’t want excuses”.

“This is the week when the carbon tax should be voted upon and should be repealed,” he told reporters in Melbourne.

Question Time this week is expected to be dominated by debate over the future of the car industry and Qantas, as well as the secrecy behind the government’s immigration policies.

But the prime minister and opposition leader won’t be taking part until Thursday, when they are expected to return to the hurly burly of Canberra.