Prime Minister Tony Abbott will personally reintroduce a bill on Monday to axe the carbon tax as his government lags Labor in the polls.

This week’s sitting is the last before the Senate changeover, after which eight mostly conservative-leaning crossbenchers will hold the balance of power.

The government wants to ram the carbon and mining tax repeal bills through the lower house by the end of this week, setting them up for debate when the new Senate sits from July 7.

However, the government has a shortage of political capital, the latest Fairfax-Nielsen poll shows.

Labor leads the coalition 53-47 in two party-terms and 47 per cent of voters rate Opposition Leader Bill Shorten as preferred prime minister – seven points ahead of Mr Abbott.

The budget remains a serious problem for the government, with 61 per cent regarding it as unfair.

A separate poll by the Climate Institute shows a softening in opposition to the carbon tax, down from 52 per cent in 2012 to 30 per cent.

Mr Abbott has invited the crossbenchers for talks on passing the government’s key policies.

“I say to the crossbench senators, if you want to save the families of Australia $550 a year there’s a very easy way – scrap the carbon tax,” Mr Abbott said.

“That’s what this parliament was elected to do.”

The prime minister said the coalition was taking climate change “very seriously” by proposing to invest $2.5 billion in “sensible, practical measures”.

Asked about the polls, Mr Abbott admitted the government was going through some “challenging times”.

Palmer United Party leader Clive Palmer will announce his position on the carbon tax repeal bills on Wednesday.

With the three PUP senators, the Australian Motoring Enthusiast Party’s Ricky Muir, Family First’s Bob Day and the Liberal Democrats’ David Leyonhjelm, the government should have enough support to repeal the tax.

Budget changes to seniors payments and welfare spending won’t have as easy a passage, with Families Minister Kevin Andrews admitting they won’t pass in time to start on July 1.

“We will obviously give people a new indication of when the changes will come in once we have some sense of what the Senate might do,” he said.

An interim report overhauling the payments system by Mission Australia chief Patrick McLure will be released in the next fortnight.

-AAP