Senator Lambie, who has famously described Mr Abbott as a "political psychopath", said on Thursday that she had not met Mr Abbott, but she had read his books.

She told ABC radio that the "last straw" for her was Mr Abbott's behaviour on the 2013 campaign trail.

"I think what really finished it off with me was when, in the last election, how he's parading his daughters around," she said.

"I'll be honest about that, because that's a security issue. That really bothers me that you've got those young girls, pretty young girls, running around in front of the camera.

"I just thought, is your political career more important than your own daughters' security?"

Senator Lambie said later on Thursday she did not regret calling Mr Abbott a psychopath and that this would not prevent her from meeting the Prime Minister.

"I have to meet him, there's no doubt about that. I have plenty I need to say to Tony Abbott. So as soon as he wants to bring that meeting forward, then that would be great," she told reporters in Canberra.

But she signalled the government would have a tough time getting measures with Senator Lambie saying she would not compromise on her opposition to the government's proposed GP fee, the deregulation of university fees or the paid parental leave scheme.

Government senate leader Eric Abetz said the new crossbenchers made the Senate manageable after months of blocks by Labor and the Greens.

The new senators were willing to make the Senate work, he said. ''At least we've got a majority in the Senate now with whom we can talk on a practical basis and not a group of senators who still resent the decision of the Australian people,'' he told Sky News on Thursday.

Senator Lambie has previously vowed to fight for her home state of Tasmania, even if it means taking a different stance on some pieces of legislation to her Palmer United Party colleagues.

She told the ABC that each of the three PUP senators had their own "head on our shoulders" that they would make the best decision for their home states.

"None of us are controlled by Clive Palmer," she said.

"All the three senators are exactly the same, they'll be fighting their guts out for their state no matter what and that's just part of the agreement with the party."

She praised Mr Palmer's economic credentials and said he was ''a good listener''.Senator Lambie said she had plenty to say and "I get my way".

She said the renewable energy target was one example of a policy that had produced different views within the Palmer United Party and she had been able to persuade Mr Palmer that there should be special exemptions for Tasmanian businesses from that scheme.

"He does agree there should be an exemption for big business, as long as it doesn't affect the solar people that have outlaid money, especially pensioners for their solar systems," she said.