She admitted on the Sunday Politics show today that parents did have concerns about the named person legislation, but that these fears were "unfounded".
It comes days after it was revealed while she will return to office as First Minister, she won't have a majority and will therefore have to seek agreement from other parties to ensure legislation is passed.
As the official opposition, the Scottish Conservatives will make abandoning the plans a priority, and during the election campaign, both Labour and Liberal Democrats said they'd had second thoughts about supporting it too.
Following her re-election, the SNP leader said she wanted to strike a consensus through Holyrood when it came to major decisions.
Her approach on state guardians - which would see everyone under 18 in Scotland assigned a named person - will be the first test of that pledge.
The Scottish Conservatives have opposed the proposal from the outset, arguing that it's an intrusion into family life and will divert resources away from those who need it most.
Scottish Conservative young people spokeswoman Liz Smith said:
"Nicola Sturgeon has made great play of being the consensus First Minister, and after Thursday's vote she will have to be.
"The first big test of this will be what she does with named person, and we will be pushing her all the way to scrap it.
"Parents and professionals across Scotland have very acute concerns about this intrusive and unnecessary legislation, so for Nicola Sturgeon to say these are 'unfounded' is quite incredible."