David Cameron arrives in Scotland on Thursday in the peculiar position of being the old Etonian Tory leader who volunteered to help set up Scotland's independence referendum and the man hated by yes campaigners for being an old Etonian Tory.

The leader of a party with just one MP in Scotland, Cameron is the bogeyman of the independence movement, instigator as prime minister of a severe austerity programme, greater NHS privatisation in England and of welfare reforms which led to the widely-hated bedroom tax and tax cuts for the wealthiest.

He is, say Scottish National party officials, one of the best recruitment sergeants for a yes vote. His government in London is the focus of Yes Scotland's final phase of the referendum: that Scotland "must" vote yes, to save itself from the Tories.

Those Westminster-driven reforms are influencing tens of thousands of Labour voters to consider backing independence, as a protest vote against a Tory-led government, helping Scotland's once disparate socialist and green left to unite in a new, highly motivated coalition, the Radical Independence Campaign.

So Alex Salmond, the first minister, knew he was touching a raw wound when he goaded Labour's Alistair Darling, leader of the pro-UK Better Together coalition which has the Tories as a significant junior partner, in Monday's BBC independence debate with the charge "You're in bed with the Tories." It is an uncomfortable alliance for the former Labour chancellor; the SNP has put him the awkward position of having to defend UK government health spending and policies.So addressing the annual dinner for the Confederation of British Industry's Scotland branch in Glasgow on Thursday night serves to amplify that problem for the no campaign.

But behind this is a more complex picture and one which presents Salmond and Yes Scotland with its own challenges: by focusing so much fire on Cameron and the Tories in a bid to attract centre-left votes, they risk creating divisions amongst Scottish voters. By implication, Scots who admire or back the prime minister and his party are enemies too.

The Tories do have a profound image problem in Scotland, and their support remains fixed at less than 20%. Yet in the last European election, the Tory vote rose slightly to 17%, even as Ukip gained historic high with 10% of the vote, winning their first breakthrough European seat in Scotland.

And the polls suggest too that Cameron is twice as popular as his party: Ipsos Mori found in August that while 15% of Scots would vote in Tory for the Scottish parliament – where the Tories have 15 seats, Cameron in person had a 30% satisfaction rating amongst voters.

Cameron's advisers insist that Salmond and the yes camp's focus on the prime minister and the Tories has little impact, portraying it as "dog whistle politics aimed at their core vote".

They argue that Cameron has played a largely very positive role in the referendum, after all, he agreed to make the referendum constitutional and fair, by granting the Scottish parliament the legal authority to stage it.

"He was the capitalist who made it happen," said one Downing Street official, who argues Cameron has helped frame a positive tone to the debate.

"He was the one to say you're no less in love with your country by wanting it to be part of something bigger" the adviser said. "His poll ratings aren't the horror story that they like to portray."

Yet that Ipsos Mori poll also exposed how greatly he is disliked: his dissatisfaction rating was at 66%. He had the highest recognition rating of all the main party leaders, a point higher than Salmond.

And so the predicament for the no campaign is – with the yes campaign putting such heavy emphasis on Tory policies in the final weeks of the campaign, whether there is a clear risk his presence will drive more wavering centre left voters to say yes in the referendum, and put even greater pressure on Labour to stop that happening. After all, Tory voters are the most committed no voters. He has no need to convert them.