Crossbench senators who are crucial to the Abbott government's success have mixed views on the impact of a Liberal leadership change.
Mr Abbott and senior ministers have blamed the Senate for blocking budget measures and other policies that would benefit the country.
Independent senator Jacqui Lambie said she would prefer talking with Foreign Minister Julie Bishop or Communications Minister Malcolm Turnbull as prime minister.
"I have no problems with either Julie Bishop or Malcolm Turnbull, which is more than I can say for Tony Abbott," she told reporters in Adelaide on Friday.
Mr Turnbull, who preceded Mr Abbott as Liberal leader, was a "gentleman" who had an interest in war veterans and had spoken to her recently about broadband policy.
"But the thing is, it's OK to say they would be (easier to work with) until they turn leader and whether or not they change their ways, that's the issue."
Liberal Democrat David Leyonhjelm said changing leaders would not solve the government's problem of being unable to convince the public of the need to fix the budget.
Former immigration minister Scott Morrison, who is also being talked about as a leadership contender, had shown in his "stop the boats" policy that a repeated message backed by action could win over the public, Senator Leyonhjelm said.
"They need to make a compelling case to the public," he told AAP.
"We do have a problem. We're spending more money than we are bringing in and there's very little scope for bringing more in."
Senator Leyonhjelm said Australia was facing the awful prospect of a one-term coalition government, followed by a one-term Labor government.
"Labor is not ready to return to government. They haven't acknowledged the mistakes of last time and are likely to make them again."
A spokesman for Family First's Bob Day said the senator had a good relationship with Mr Abbott and knew him very well.
But he would work with whoever was prime minister.
The government needs six Senate crossbench votes to pass its legislation.
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