Yet the SNP hit back, claiming the Unionist parties were "obsessed" by the second question issue and insisted the demand for one was not coming from the First Minister.
Speaking during a Commons debate, David Mundell, the Scotland Office Minister, stressed the SNP won its landslide victory in the Scottish parliamentary elections last year on the basis of a manifesto commitment to hold a referendum on independence – not on further devolution.
He told MPs if there were a U-turn in putting a second question on the ballot paper, it would be "an upfront admission of defeat, an acknowledgement that the First Minister believes he cannot win a single question referendum".
During the debate, the SNP's Mike Weir, who represents Angus, accused the Unionists of being "obsessed" by the issue of a second question.
An opinion poll revealed by The Herald this week showed support for independence was at a low of 30% compared with opposition at 50%.
When a third option was put in a second question, support for extra powers rose from 30% to 37%.