Official forecasts show debt in relation to wealth is set to reach its height in 2015/16, not a year later as previously forecast.
The independent Office for Budget Responsibility (OBR) has also downgraded its estimates of future oil and gas revenues by almost £4 billion over the next three years.
Alistair Darling, the former Labour Chancellor and chairman of the Better Together pro-Union campaign, said: "After the publication of the Scottish Government's White Paper on Independence I said [the SNP] were being wildly optimistic about debt and these figures prove that."
He added that lower oil and gas revenues would mean the government of an independent Scotland "would have a bigger gap to fill".
But a spokesman for Scottish Government Finance Secretary John Swinney said: "An independent Scotland will be in a healthier financial position, on any measurement, than the rest of the UK - and of course will also be entitled to a fair share of UK assets, as well as liabilities."
Mr Swinney had himself earlier rejected the OBR analysis saying the oil forecasts were not consistent with industry expectations. He added: "Scotland has a vibrant oil and gas sector and will continue to do so for many decades to come."
That view was backed by the leader of the industry body, Oil & Gas UK. Malcolm Webb said his organisation took a less pessimistic view than the OBR estimates.
He said it was "encouraging to know the government is committed to maximising economic oil and gas production offshore, and shares our welcome for the interim findings of Sir Ian Wood's review".
He added: "With up to an estimated 24 billion barrels still to be recovered there is a strong future for the North Sea, but as a mature basin, this will require, among other measures, an encouraging fiscal regime if the recovery of our oil and gas resource is to be maximised."
The updated OBR figures forecast around £1.7bn less in revenues from oil and gas next year alone, compared to its previous estimate in March. The organisation put the revisions down to changes in oil prices.
As part of his Autumn Statement, the Chancellor announced that debt was set to peak as a proportion of gross domestic product (GDP) - a proxy of a country's wealth - just as the Scottish Government hopes to complete pre-independence negotiations.
The Chancellor said: "At the Budget, the OBR forecast debt to be falling on 2017-18. It is now forecast to fall in 2016-17 - that's one year earlier."
The OBR forecasts debt will be 75.5% of GDP this year and will rise to a peak of 80% of GDP by 2015-16. It will then start to fall although it is expected to take years to return to 2012-13 levels.
The OBR confirmed last night that while debt would fall as a proportion of GDP it would still continue to rise in money terms.
The Scottish Government has said it plans to negotiate the details of an independent Scotland's separation from the rest of the UK in time to officially declare independence on March 24, 2016,
Mr Osborne also used the Autumn Statement to announce plans to permit local authorities in Scotland to access up to £250 million cheaper borrowing at the Public Works Loan Board. This is on top of the £2.3bn of capital borrowing powers the Scottish Government will get in 2015-16 as a result of the Scotland Act.
Also announced was a payment of £10m to wipe out Shetland Islands Council's historic housing debt. The move was welcomed by Shetland council, which said it wanted to thank local Alastair Carmichael, the Liberal Democrat Scottish Secretary "who has worked so hard on our behalf".
The UK Government also said 330,000 couples in Scotland would benefit by up to £200 a year through a marriage tax break.
Mr Carmichael said: "As part of the UK, Scotland is benefiting from the measures we are taking to get our economy growing again."
The Scotland Office also said that the abolition of employer National Insurance contributions for under-21s could save businesses in Scotland £45m and support the jobs of 138,000 young people, while the cancelling of next year's planned fuel duty rise would help the drivers of 2.7 million vehicles in Scotland.
A roll back of "green" energy taxes is also forecast to help more than 2.5 million households, who should see an average of £50 cut from their fuel bills.