The prime minister said the referendum was nothing to do with his future or that of the Scottish first minister, Alex Salmond, but is a clear choice for Scots between staying or going.
Asked on BBC Radio 4's Today programme whether he would resign, Cameron said: "I think it's very important to say no to that emphatically for this reason: that what is at stake is not this prime minister or that prime minister, or this party leader or that party leader. What is at stake is the future of Scotland … I think it is very important for people in Scotland to realise the consequence of their vote is purely and simply about Scotland and its place in the United Kingdom.
"We shouldn't try and tie up in this vote the future of Alex Salmond or me."
Despite Cameron's claims that his position is irrelevant, many in the no campaign fear the threat of him winning the next election could encourage people to vote yes.
The Scottish Conservative leader, Ruth Davidson, has even talked down Cameron's chances of winning next year's election, with an apparent awareness of his unpopularity north of the border.
On Thursday morning, Ed Miliband stepped up his own campaign for the union, promising Scots a Labour government was on the way.
"The Labour party is taking the fight to the SNP, particularly in these last two weeks," he told BBC Radio Scotland.
He accused the Scottish nationalists of falsely trying to argue that "the Tories can't be beaten".
"That is absolutely the opposite of what is happening. You've got a Tory government where its MPs are defecting; it is divided, it is downhearted," he said,
Cameron has always acknowledged that he is not the best person to advocate the union and has not played a leading role in the no campaign.
However, he said he would be making a bigger intervention in the debate in the coming weeks.
"This is a desperately important question," he said. "I care passionately about it. It would break my heart if Scotland were to leave the UK but I absolutely believe it is right to give people in Scotland the choice."
Cameron has previously indicated he would not resign in the face of a yes vote but he would be likely to face calls to go in that event as he could be held responsible for the breakup of the 300-year union.
He is also likely to come under pressure to postpone next year's UK general election by 12 months in the event of a vote for Scottish independence, in order to avoid the prospect of a Labour government that would depend on Scottish MPs.
The most recent polls have suggested that what was a strong lead for the no campaign has been significantly eroded.
Following the YouGov poll, which shows a six-point lead for the no camp, the pound fell in value against other currencies as investors and traders took fright at the prospect of the union breaking up.
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