It comes after Ms Sturgeon took to Twitter to defend her party's Growth Commission which was published last week and has caused ructions among left-wing SNP supporters over its plans for a decade of spending curbs after independence.
But the SNP leader hit back insisting that only the Tories and Labour regularly raised the constitution in the weekly grilling at First Ministers Questions and reeled off a list of domestic actions taken by the Scottish Government this week.
"Does she wonder why the people of Scotland question her (Ms Sturgeon's) priorities?" the Tory leader said.
"This week alone we have learned that 17,000 people in just a single month are waiting beyond the six week deadline for diagnostic tests including cancer.
"It has become harder for young people from our poorest communities to get a place at University and we have communities right across Scotland suffering from rising antisocial behaviour and violent crime
"These are the important issues that the people of Scotland really care about. So why is it that the only folk getting any of the First Minister's attention aren't patients, they aren't students, they aren't victims of crime - they're her own independence supporters?"
The First Minister also said the past 24 hours had seen her announce £5 million of investment in an engineering "centre of excellence" in Montrose, as well announcements for a new Scottish manufacturing institute, while she has also held discussions on inward investment in tourism, energy and low carbon technology.
She added that more money is going into the national health service in Scotland.
"This is in the week that Ruth Davidson admitted that the biggest risk to our health service was the preference of the Tories for tax cuts over investment in public services.
"And perhaps this is a good moment to remind Ruth Davidson if we had taken her advice when we published our budget for this financial year and given tax cuts to the rich instead of investing in our national health service, we'd have £500 million less to spend.
"That's equivalent to 1200 nurses. So we will continue to invest, while the Tories continue to do all the damage."
Labour leader Richard Leonard also hit out hit out the NHS waiting times, insisting that one in five patients now wait too long for key diagnostic tests, including for cancer, compared with one in 23 when Ms Sturgeon became First Minister.
"That is what the people of Scotland want the First Minister to focus on," he said.
"Not promoting another divisive referendum, not taking to Twitter to defend the decade of cuts and austerity that would come with leaving the UK."
He added: "When is the First Minister going to stop putting nationalism before the National Health Service?"
Ms Sturgeon hit back: "The only people to have mentioned independence in this chamber today are the Better Together parties."