Sturgeon said so in a speech to mark a year since the referendum in Edinburgh on September 18, 2014 when Scotland had voted by 55 per cent to 45 per cent to remain a part of the UK.
She said "My message to David Cameron today is the same as it was when I met him just after the general election.
"What happens to support for independence in the months and years to come will depend as much on what you do as it will on what we do. And, right now, you are living on borrowed time.
Meanwhile, Cameron outlined plans to guarantee the permanence of the devolved Scottish Parliament.
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"Alex Salmond, Nicola Sturgeon and I signed the Edinburgh Agreement which pledged we would all respect the outcome of last year's momentous vote.
"We all agreed - as do the Scottish public - that the independence referendum should be a 'once-in-a-generation' or a 'once-in-a-lifetime' event. So, now it is time to move on," he said.
The first will change the wording to put beyond doubt that the Scottish Parliament is a permanent part of the UK's political constitution.
The second amendment will state that the Scottish Parliament can only be abolished with the agreement of the Scottish people in a referendum.
Sturgeon's pro-independence SNP has been on a popularity surge, with her approval as party leader at an all-time high.
The party won an unprecedented 56 out of 59 Scottish seats in the UK general election, making it the second largest party in Westminster after the ruling Conservatives.