The £70-worth of savings on the average energy bill was the most high-profile announcement from this year's SNP conference.
At the time Scottish ministers said the policy would be funded in part by money from the EU's Emissions Trading System (ETS).
But ETS was not mentioned in the 650-page blueprint for independence last week.
Labour have accused Scottish ministers of realising that their plans were an "empty promise".
The party also warned that the pledged £70 cut would create a £400 million black hole in an independent Scotland's finances.
Labour said that the policy would cost around £466m, while Scottish ministers would raise just £67m from ETS. The calculations are based on the party's analysis of figures from the House of Commons library.
Shadow energy minister Tom Greatrex, the MP for Rutherglen and Hamilton West, said: "The SNP's energy policy is falling apart under scrutiny.
"Alex Salmond's plans to shift some social levies into general taxation and fill the gap with funding from the EU ETS scheme is another empty policy promise - and exposes a separate Scotland to a £400m green hole to fill."
He added: "The flagship policy from the SNP's conference has unravelled to such an extent that despite [Deputy First Minister Nicola] Sturgeon's hyperbole, the SNP have dropped any mention of funding for the proposal from 'Scotland's Future'."
In the independence White Paper Scottish ministers do not mention ETS though they say they would cut bills by transferring responsibility for a number of 'green' energy schemes from power companies to the Scottish Government.
A Scottish Government spokesman said: "These claims are completely wrong - 'Scotland's Future' makes it abundantly clear that these schemes will be funded from central resources if this administration is the first Government of an independent Scotland, saving the average household around £70 per year."
Labour warned energy bills could rise after independence as Scotland would lose UK state support for renewable energy.
"And in terms of renewable costs, the simple fact is that the rest of the UK is going to depend on Scotland's huge energy resources, including green energy, to keep the lights on in the years to come," the Scottish Government spokesman said.