The scheduled no-confidence debate has been postponed by parliamentary Speaker Baleka Mbete, who has said she has no powers to agree to a secret ballot.
"I think the court will rule in our favour", Singh told reporters during an adjournment by the Constitutional Court.
There is no risk for MPs who openly vote against President Jacob Zuma if they truly believe they have lost confidence in him, his lawyer argued in the Constitutional Court on Monday.
An ANC MP said there were a significant number of MPs who were prepared to vote with the opposition to get rid of the president, as they could no longer defend his administration.
Despite growing dissatisfaction with Zuma's leadership in the ruling African National Congress, which holds a 62 percent majority in parliament, the party's leadership has rejected all opposition-led attempts to remove him.
"Any member of parliament may vote on any topic according to his personal conscience".
Opposition parties hope this would encourage enough ANC MPs to vote against Zuma for it to succeed.
"Our case is very simple".
Dali Mpofu, for the UDM, implored the court to look at the section in the Constitution which explains the goal of the protection of a secret ballot.More news: Hong Kong rejects asylum for refugees who sheltered Snowden
"Why is it that the constitution prescribes a secret ballot?"
"What would explain this court's position that you have a discretion but we are telling you now that it must be by secret ballot".
UDM advocate Dali Mpofu SC said the only question which arose in this case was whether the meaning of an expression "a vote" in section 102 meant whether a secret ballot was impliedly required‚ or permitted or prohibited.
"She has an obligation to choose a voting method when asked to do so, she has abdicated to do so".
The president and Mbete are asking for the application to be dismissed.
Zuma retains widespread support from ANC members in some rural areas and has been able to rely on lawmakers to survive previous votes of no confidence.
The hearing brought to the fore the issue of separation of powers, and whether the highest court in the land had the prerogative to request Mbete to schedule a secret ballot against Zuma. If they say the secret ballot is permissible, there is an obligation on Parliament to sanction it. In a ruling past year, the Western Cape High Court dismissed an application that sought to force the National Assembly to hold secret votes on no-confidence motions.
In his heads of argument‚ counsel for Mbete, Marumo Moerane SC said Mbete was open to persuasion by political parties to consider that voting be allowed by way of secret ballot. But Justice Mogoeng said the constitutions of those countries made provisions for a secret ballot, while the South African one did not. "There could be consequences for this", he said.