Former Nationalist depute leader Jim Sillars, a veteran of the independence movement, said there was now a division within the SNP between the majority of supporters who believe there will be a vote before 2020 is over and the minority of those who do not.
The First Minister will this week call on the Scottish Parliament to back an IndyRef2 being staged in 2020 in a landmark vote.
But that move has been branded a “waste of time” by pro-Union MSPs.
Mr Sillars, a one time MP for Govan, said SNP members should instead be working to "convert" those who are not behind Scottish independence, rather than "marching every weekend" - a reference to recent All Under One Banner (AUOB) marches across Scotland which have attracted tens of thousands.
Ms Sturgeon and Westminster leader Ian Blackford have been among the party leaders who say they want to see another vote soon, despite the rejection of the Prime Minister to devolve the necessary powers.
Mr Blackford has accused Boris Johnson of "denying democracy" for his refusal to grant a request for a section 30 order. A spokeswoman for the party said there was a "resounding democratic mandate" for another poll.
Writing in the Scottish Daily Mail, Mr Sillars said: "That 45 per cent can march every weekend, while the Unionist majority goes shopping and remains unpersuaded.
"We in the minority know it is those shoppers we need to discuss things with, in a civilised manner, and convert. A longer process than a few months; and one that cannot have any worth until we know the final details of the Brexit negotiations."
The former deputy leader also questioned if there was enough "intellectual rigour" in the arguments for another referendum.
He said: "In my political apprentice years, I was taught by old school socialists that the application of intellectual rigour was an essential mental tool when considering policies.
"That quality is sadly missing, if it ever was there, in today's SNP leadership.
"Just a few minutes' study of the idea of an illegal referendum that scrapes past the courts (most unlikely) shows what a nonsense it is. The Unionist majority will take no part, so the SNP ends up with a majority of a minority. What happens then? I have yet to learn of plan B."
An SNP spokeswoman said: "Scotland is due to be dragged out of Europe against its will in a matter of days - in those circumstances we are determined to give the people of Scotland a choice on the country's future in an independence referendum.
"There is a resounding democratic mandate for a referendum, and the longer that Boris Johnson tries to block it the more that support for a referendum, and for independence, will continue to grow across Scotland."
On Sunday, pro-independence think tank Progress Scotland released a poll suggesting Scots would like Holyrood to have the final say on whether a vote should be held.
The group, set up by former SNP Westminster leader Angus Robertson, found that 61% of the 1,019 respondents who expressed an opinion believed that the Scottish Parliament should make the decision on another vote.
SNP leaders have been pushing for another vote since the General Election in December, which saw the party win 47 seats north of the border.
After laying out the "democratic case" for another referendum, the First Minister sent an official request for a Section 30 order to Westminster - which was rejected by the Prime Minister this month.
Ms Sturgeon will lead a debate on Scotland's future on Wednesday, where the Parliament will be asked to back the mandate for another referendum, before laying out the "next steps" for Scottish independence on Friday - the day the UK is due to leave the European Union.