Mr Salmond has responded to critics who say he has "all the powers he needs to deliver better childcare" under devolution.
A YouGov poll, commissioned by pro-UK campaign Better Together, found that nearly two-thirds of people believe the Scottish Government should use its current devolved powers to provide better childcare.
Over a fifth think Mr Salmond needs independence before he can deliver better services.
The Scottish Government said it has already delivered in this area, offering 600 hours a year under the SNP, compared with 412 hours under Labour
The SNP said it could provide nearly twice as many hours with independence, initially funded by diverting money from nuclear weapons to childcare and sustained by taxes generated by the consequent rise in the female workforce.
Mr Salmond said: "Our plan is to move to broadly the same number of hours of nursery education as children currently receive in primary school - the equivalent of 30 hours per week for 38 weeks, or 1,140 hours a year. That would allow most women with families the opportunity to get back into the workplace.
"People ask why we can't simply introduce these plans now.
"The problem is that the increased tax revenues which would be generated by thousands of women returning to work, as well as the reduced level of welfare payments they currently receive, would be lost to Scotland and go to Westminster instead.
"Under independence, that money would stay in Scotland to help pay for the expansion of childcare on a sustainable basis.
"An increase in the number of women in work of just 2%, taking us above the number of women at work in the Netherlands, for example, would boost tax revenues by £200 million.
"If the female activity rate reached Swedish levels - a 6% increase in the number of women at work - tax revenues would increase by £700 million and the number of women in the labour market would rise by 104,000."
The YouGov poll found 64% of respondents who said Alex Salmond and the Scottish Government should use the powers they already have to deliver better childcare, while 22% said they would need a yes vote in the referendum.
Scottish Labour Leader Johann Lamont said: "Alex Salmond could act today to provide parents with better childcare, but would rather use it as a false argument for breaking up the UK now."
Conservative young people spokeswoman Liz Smith said: "Alex Salmond already has all the powers he needs to deliver better childcare, so there was never any chance that he could fool the public into thinking it was just a special flagship policy for the referendum."
Liberal Democrat leader Willie Rennie said: "Parents need to see SNP ministers spending less time talking about the powers they want and more time using the ones they already have to help children get the best start in life."