As the Senate changes, the federal government is gearing up to negotiate its key election promises through the upper house.

They’re not a motley crew, they’re God’s children.

That’s the attitude that the government is taking into the Senate, where the numbers change from Tuesday.

The Abbott government will need six votes from the eight-member crossbench, Labor or the Australian Greens on top of its 33 members to get legislation through the Senate.

Government Senate Leader Eric Abetz, whose role will be to secure the six extra votes, said he wouldn’t describe them as a motley crew.

“They’re all God’s children as far as I’m concerned, but we will be working with them on the issues, case-by-case,” Senator Abetz said.

While the government is confident of passing the carbon tax repeal bills relatively soon after the new Senate sits from July 7, Prime Minister Tony Abbott has put at least one of the new senators offside.

Palmer United Party Senator Jacqui Lambie, from Tasmania, would axe the carbon tax but is concerned Mr Abbott has not replied to her other concerns.

“I don’t think Tony Abbott is a very good leader,” she said.

“I’ve already sent 12 official letters to the PM over the last nine months. I haven’t had one response and I find that very disrespectful.”

Greens leader Christine Milne, who now heads a team of 10 senators, said her party was experienced at working with others to get outcomes and would focus on retaining the emissions trading scheme.

New Greens Senator Janet Rice supports her party’s opposition to the reintroduction of fuel tax indexation, which will be debated by the new Senate.

But if the government agrees to put the revenue raised towards public transport “it would be something we could support”, she said.

Dealing with the Senate was a key agenda item for Prime Minister Tony Abbott as he chaired cabinet in Canberra on Tuesday.

Also weighing on ministers’ minds was the latest Newspoll, which put Labor 10 points ahead of the coalition in two-party terms and delivered Mr Abbott a 62 per cent voter dissatisfaction rating.

“It hasn’t been easy. There’s been lots of political ups and downs but nevertheless those fundamentals that we made a commitment to the public on we are delivering,” Mr Abbott told the meeting.

The government will step up its lobbying of the crossbench to get around Labor and the Greens’ opposition to the reintroduction of fuel tax indexation, the Medicare co-payment, higher education deregulation and a raft of pension and welfare measures.

Mr Abbott said the carbon tax would be abolished “in the next week or so”.

Opposition Leader Bill Shorten said Mr Abbott’s main failing had been not building a consensus around his agenda.

“Tony Abbott has a Downton Abbey style of consensus – he summons Australians like a servant class to agree with his consensus,” Mr Shorten told reporters in Canberra.

He said the “far right” had spread doubt about the science of climate change and Labor would need to “refight” the case for action.