Employment Minister Eric Abetz is confident a challenge against unions royal commissioner Dyson Heydon won't succeed.
Mr Heydon was due to deliver a ruling on Tuesday on a unions bid to have him disqualified from being commissioner.
But a spokesman said on Monday the former High Court judge was going to take more time to consider the ruling.
Senator Abetz declined to say whether the government had a "Plan B" in terms of replacing Mr Heydon should he decide to step aside.
"All I'm saying is one step at a time," he told ABC TV on Monday.
"We believe that Dyson Heydon is a very good choice for this royal commission, that he has done an outstanding job, and this campaign of vilification against him ... there is no substance to it at all."
He said the campaign against Mr Heydon was "motivated by venom and hatred".
Union lawyers told a hearing last Friday Mr Heydon would have been well aware that he had accepted an invitation to speak at a Liberal Party event.
The flyer promoting the event, which had been emailed to the commissioner's office, used the Liberal Party logo and said funds would go to "state election campaigning".
Labor frontbencher Penny Wong said Mr Heydon should "do the right thing".
She said his comments made on Friday did not allay public concerns.
"I don't think any fair-minded observer, looking at the explanations he has given for his acceptance of speaking at a Liberal Party fundraiser, could come to the view that there is no apprehension of bias," Senator Wong said.
A public hearing scheduled for Wednesday involving the CFMEU NSW branch has been postponed indefinitely.
Prime Minister Tony Abbott said Mr Heydon wanted to carefully consider the union submissions in his usual "meticulous" way.
"He doesn't want to get it wrong. He wants to treat the submissions with respect," Mr Abbott told 2UE Radio on Monday.
But he said the royal commission must go on whatever the decision of the former High Court judge.
"There is an absolute need for this royal commission," Mr Abbott said.
ACTU secretary Dave Oliver said in a statement the delay in Mr Heydon's decision did not stop Mr Abbott from taking action.
"The ACTU has always maintained that the prime minister must shut down his political witch hunt and stop wasting millions of dollars in taxpayers' money," Mr Oliver said.
"The ACTU again calls on Tony Abbott to act immediately."
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