Former minister Arthur Sinodinos says his support for Prime Minister Tony Abbott is not without conditions.
Senator Sinodinos, a former chief adviser to prime minister John Howard who stood aside as assistant treasurer to deal with NSW anti-corruption commission matters, is considered a strong supporter of Mr Abbott.
The NSW senator told Sky News on Wednesday that leadership speculation was "not just media hype" and needed to be sorted out.
Some MPs want a vote brought on as early as next Tuesday, when the party room meets for the first time this year.
Senator Sinodinos said he had always supported Mr Abbott, but it never came without conditions.
"My support for him has been based on his performance, his courage, his capacity to make the right calls for the country in opposition and in government," he said.
"But that support ongoing is not unconditional.
"It's based on being able to grapple with the issues we face at the moment which appear to have impacted on our standing in the polls."
The senator said it should be considered more than a personality contest between alternative leaders.
"We need to work out what it is we need to fix," he said.
Senator Sinodinos said it was hypothetical whether Julie Bishop or Malcolm Turnbull would be a better leader because "no one has put their hand up".
He said the government needed to show voters it was in touch with public concerns.
Asked about the future of the Medicare co-payment, he said the government should not spend the next six months talking to doctors and trying to redesign it.
"I think we either design one that is appropriate and equitable or we drop the concept and look for other ways to restrain health spending."
He also argued the government should be generous to pensioners, but do it in a prudent way without blowing out the budget.
However, he stood by the plan to deregulate universities.
"I think that is a worthwhile reform," he said.
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