David Cameron is considering basing himself in Scotland for much of the last two weeks of the Scottish referendum campaign, in a move opposed by Liberal Democrat cabinet colleagues who say he could damage the no campaign.

Liberal Democrat figures privately insist that Cameron is a huge negative in Scotland and should stay out of the country as much as possible ahead of the 18 September poll.

One Liberal Democrat cabinet member said: "We have been told he wants to spend as much as possible of the last two weeks in Scotland, especially if there is a clear lead for no, and so he can pose as the man that saved the union."

Downing Street said Cameron would be in Scotland in the run-up to the referendum, but gave no timetable, pointing out that he has no vote in the referendum and many other commitments as the UK's prime minister.

Cameron himself promised in an ITN interview to make an emotional as well as an intellectual case for Scotland to remain within the UK.

An STV debate on 5 August, days after the end of the Commonwealth Games, between Scotland's first minister, Alex Salmond, and Alistair Darling, the leader of the pro-union Better Together campaign, will signal the start of the final run-in. The deadline to apply for a postal vote is 3 September and the Westminster government does not return until 12 September, giving Cameron considerable scope to spend time in Scotland before referendum day.

Cameron was in Glasgow on Wednesday for the opening ceremony for the Commonwealth Games, and attended a Commonwealth business event where he vowed to avoid politics during the ceremonies.

In his ITN interview, however, he said that "if Scotland leaves the UK, then Scotland is leaving the pound" and added that he had "never made the argument that Scotland couldn't exist as an independent country".

He said: "A no vote would provide Scotland with the best of both worlds. Scotland can decide its own health, its own education, its own policing, its own criminal justice and yet it can have the strength of the UK. And that's a positive case."

The Commonwealth Games are seen as one of the last chances for Salmond to generate an emotional patriotic mood ahead of the poll. He described Glasgow as the "freedom city", meaning he believes it will vote for independence.

He described the Games "as the greatest festival of sport Scotland has ever seen".

Senior figures in the Better Together campaign believe the only serious danger of defeat is if Salmond can generate an emotional mood for independence in the final weeks, claiming the Scottish National Party (SNP) has lost most of the policy arguments.

Cameron said: "I've always made the argument of the heart as well as the head. We mustn't allow the nationalists to own the romance of having a strong Scottish identity. The great thing about the UK is you can hold several identities at the same time and they don't have to compete with each other, but yes, I absolutely agree that in the closing weeks of this campaign we should make the arguments about what the United Kingdom has done in the past - everything from defeating the Nazis to inventing the health service - and we will make the arguments about what we can do in the future. And we must make emotional arguments as well as rational positive arguments."

He defended his right to be campaigning to keep Scotland as part of the union despite his party's unpopularity in the country.

He said: "I think that people in Scotland do want to hear from the United Kingdom prime minister about issues that affect the whole of the United Kingdom. I've tried to play my role in this campaign recognising that in the end it is for Scottish people to decide - I don't have a vote - but I feel passionately about the United Kingdom and I won't be voting in that election but I hope those that do vote to stay together".

Salmond has also promised to avoid talking about the referendum for the duration of the Games, but he was unable to stop himself from saying to the 71 nations and territories of the Commonwealth that a yes vote was nothing for them to worry about, pointing out that many of them have secured their own independence from UK rule.

The no campaign insists they are not complacent ahead of the referendum despite the polls pointing in their favour, but point out that there is no sign the remaining undecided voters are breaking disproportionately for the yes camp.

Douglas Alexander, the shadow foreign secretary, said: "What is remarkable is not how much the polls have shifted, but how little. The quiet but resolute majority of Scots continue to say 'no thanks' to separation.

"With weeks to go until 18 September the nationalists are running out of time, running out of road, and running out of arguments. The task between now and 18 September is bringing home the vote, the task after the referendum is bringing Scotland together."