The election of an Scottish National Party (SNP) majority government brought about massive strategic changes on behalf of the unionist parties. For decades the latter had done everything possible to keep independence off the agenda. Now they wanted an independence vote as soon as possible believing that this would undermine the SNP cause. Many spurious reasons were given for this demand, such as investment in Scotland being harmed by the uncertainty a long campaign would create, but the main reason was to call the SNP's bluff. Support for independence in opinion polls was consistently around 30% - 35%, and defeating independence at the polls would lay the issue to rest for a generation.
The unionist parties could have forced through a vote since Westminster had reserved powers over all constitutional matters under the 1998 devolution Act. As Westminster Secretary of State for Scotland, LibDem MP Michael Moore, noted, it would be illegal for the Scottish Government to hold a referendum. There again, Westminster holding a referendum on its own terms may be legal but viewed as gerrymandering (that is, the powerful trying to fix the outcome in their favour). When such top-down elections have been tried in the past (in Northern Ireland over membership of the UK) the side 'destined' to lose have simply refused to vote thereby making the process a farce. Like it or not, to have meaningful and lasting authority any referendum would have to involve the Scottish Government.
Having just won a landslide victory it could be assumed the SNP would also have wished for a quick referendum, but success plunged the party into its own crisis. Aware that losing an independence vote would bring the very existence of the party into question, some SNP members wanted a more gradualist approach, so the priority would be to secure more powers for the Parliament ('Devo Plus' or 'Full Fiscal Autonomy' – ‘Devo Max’) rather than immediately testing the Scottish public on its willingness for independence. However, the party leadership were aware that having won power as pro-independence party they could do nothing but hold a referendum, as this had been their goal since foundation in 1934. A proposed compromise was to have a 'double question' on the ballot paper asking whether the voters wanted full independence (yes/no) or some form of 'Devo Plus' (yes/no).
Take your learning further
Read this article from the Guardian newspaper which looks at the concept of a Westminster-led referendum.