First Minister Alex Salmond has demanded a "guarantee" from the Prime Minister that Scotland's budget would not be slashed in the event of a No vote to independence, amid fears of a £4 billion cut.

The First Minister wrote to David Cameron after Westminster's All Parliamentary Taxation Group published its first report on the implications of the referendum last week. The powerful cross-party group recommended that if Scots voted No, the Barnett Formula which sets Scotland's budget and guarantees a higher per capita spend than the UK average, should be scrapped.

They wrote: "In the case of a 'No', the Barnett Formula must be replaced as a priority, with a needs-based formula ... using the seven indicators of relative need identified by the [2010] Holtham Commission [on Welsh funding]." The chair of the Holtham Commission, Gerald Holtham, suggested in 2010 that replacing Barnett with a formula similar to the one used to set funding in England "could eventually result in Scotland getting as much as £4bn less than it currently does".

Raising this in his letter to Cameron, Salmond said: "To bring clarity to the debate so that people understand the consequences of a No vote, I would be grateful if you would give a guarantee that no future Westminster government will scrap or review the Barnett Formula or cut Scotland's share of spending."

In practice, as Salmond knows, no Westminster government could give a guarantee that would bind its successors in perpetuity to not altering the Barnett Formula. However, it fits with the SNP plan to run a twin-track campaign on the referendum: promising benefits with a Yes vote, while warning of Westminster harm in the event of a No.

Referring again to the MPs' taxation group, Salmond went on: "Westminster parliamentarians are publicly calling for spending in Scotland to be cut by as much as £4bn - equivalent to £1600 for every income tax payer in Scotland - and the implications of this devastating report for Scotland's public finances in the event of a No vote could not be clearer."

In a dig at Cameron's refusal to meet him in a TV debate, Salmond ended: "It is surely now time for you and I to debate these and other matters in order that voters in Scotland can judge the arguments for themselves."

Nicola Sturgeon, the Deputy First Minister, said the White Paper's plan for a transformation of childcare - doubling provision to 1140 hours for all those aged three and four in the first parliamentary term after a Yes vote - was not possible in practice under devolution. She said: "We can create a virtuous circle in which transforming childcare frees women to work, generates more tax revenue and helps to fund the further expansion in childcare. But it is only by having both sides of the balance sheet - revenue and spending - that we can deliver the help people need.

"The devastating cuts being imposed now, and the additional £4bn cuts planned by the Westminster parties, mean the only way to do this under devolution would be to cut key gains of devolution: funding for care of the elderly; funding for free university education; or funding for the childcare that people need."

Professor Ailsa McKay of Glasgow Caledonian University, whose research underpinned the policy, said it would stimulate economic growth, increase female participation in the workforce, and improve children's wellbeing. "The gains of investment are greatest for the most deprived children," she said. "In addition to the educational gains, which in turn lead to gains in earnings, there are also behavioural gains and increased civic and social engagement."

A Downing Street source was dismissive of the FM's request for a never-ending guarantee, saying: "As the Institute for Fiscal Studies and others have pointed out, the biggest threat to Scotland's fiscal position is independence."

The White Paper's initial print run of 20,000 copies is to be extended, with 10,000 extra copies of Scotland's Future ordered, with more likely to be printed after 2.5 million postcards go out to every household next week with details on accessing it.

Since Tuesday's launch, the paper has also been downloaded almost 70,000 times as a PDF file and more than 30,000 times as an eBook. There have been almost 370,000 page views on the Government's main website and another 100,000 on the dedicated scotreferendum site. The Government has also taken more than 11,000 phone calls and received 10,000 emails from people requesting hard copies.

A summary version has been translated into 13 languages, including Mandarin and Russian.

The Scottish Tories highlighted a proposal in the White Paper to give the police the power to conduct "random breath tests anytime, anywhere".

Transport spokesman Alex Johnstone said: "It's an indication that an independent Scotland would shift towards becoming a police state."