They said that the UK Government's chief campaign co-ordinator was "staggered" by the lack of detail coming from the Scottish Government.
A Whitehall insider likened the battle to "professionals versus amateurs".
The SNP has accused the UK Government and high-profile ministers including Mr Osborne, of "scaremongering" over independence.
The Chancellor chairs the Coalition's cabinet committee on Scotland, which co-ordinates its push against independence.
It has faced criticism after a preview of a Whitehall paper on separation warned of the possibility of mobile phone roaming charges between Scotland and England, despite the issue being tackled by the EU.
While polls suggest most Scots oppose independence, First Minister Alex Salmond has described recent debate on the issue as the "phoney war" and insisted his party's referendum campaign had yet to begin.
But Downing Street sources made clear that the Chancellor believed his campaign was "going much better than any of us could have hoped. We have created that debate".
They said it could not have been predicted "that the SNP would have so few answers," describing it as "staggering".
Mr Osborne is also understood to believe that the fight to keep Scotland in the Union is "one of the most important things that is happening in this parliament."