UK Government insiders said the SNP's timetable for EU negotiations would limit the party's ability to get a good deal for Scots.
But the Scottish Government hit back, accusing the Tory- LibDem Coalition of trying to "cover" over its own splits on Europe.
The SNP says the real threat to Scotland's EU membership comes from the UK Government, after David Cameron pledged an "in-out" referendum in 2017 – a policy opposed by his Liberal Democrat Coalition colleagues.
Ms Sturgeon, who at the weekend also attacked pro-Union claims Scotland would get extra powers if it rejected independence, will be grilled about an independent Scotland's EU membership by the House of Commons Foreign Affairs Committee today.
The Scottish Government says Scotland will take part in EU talks from within the UK – but it has also set a target for Scotland to be fully independent by 2016.
Coalition Government sources said 2016 was a very tight timetable to finish two sets of talks – one with the EU and the other with the UK Government.
A Downing Street source said it was highly unlikely talks on a range of EU issues, such as the euro, would be resolved by 2016.
"Either [talks] won't be concluded or the SNP are going to have to give up a hell of lot," he said. He added that if talks were not completed by then, Scotland could still be part of the UK "during the Scottish Parliament elections in 2016 and after,"
"What does it mean then if another party wins that election? And how would the rest of the UK feel about Scotland staying part of the UK for years and years when it had already made clear in a referendum that it wants to leave?"
The UK Government last week rejected Ms Sturgeon's call for a joint submission to the EU, after the European Commission snubbed her calls for talks.
A spokesman for Ms Sturgeon said No campaigners were "trying to cover up their own splits and divisions over Europe with more baseless claims."
She added that Scots were EU citizens and there was no provision to change that fact upon independence. "If the UK Government thought there were genuine concerns, it should work with Scottish ministers," she added.
It also emerged that Lucinda Creighton, Ireland's Minister for European Affairs, had written to Ms Sturgeon saying comments she made to the BBC about the EU – in which she said Scotland would have to "apply for membership, and that can be a lengthy process" – had been misconstrued.
She wrote: "I certainly did not at any stage suggest that Scotland could, should or would be thrown out of the EU".
The BBC said it stood by its story.
A poll at the weekend showed 60% of voters believe an independent Scotland would not automatically become an EU member.
But the Yes campaign yesterday hailed figures from the same poll, saying they showed they needed an achievable swing of 7% to win.
Yesterday, Ms Sturgeon also questioned David Cameron's pledge that Scotland would get extra powers if it rejected independence. "A 'No' vote would relegate Scotland to the bottom of the Westminster agenda,' she said. "The idea that Holyrood would gain new powers in these circumstances is fanciful."
A source close to LibDem Scottish Secretary Michael Moore said: "The SNP is the only party that had refused on every occasion to take part in planning the devolution of power from London.
"The Nationalists should spend less time trying to distract people with this negative talk and more time explaining how an independent Scotland would negotiate its way into the EU, afford new defences and regulate its banks."
Scottish LibDem leader Willie Rennie has invited Ms Sturgeon to take part in talks about the shape of future extra powers.
Last night, the Electoral Commission refused to comment on reports that it was poised to reject the SNP's proposed wording of the referendum question.