Two-fifths of Scots are against independence, the new poll by anti-independence campaign Better Together suggests, but 33% said they would be less likely to back it if Scotland had to join the troubled single currency.
The percentage is slightly higher amongst SNP supporters (34%) and higher still amongst Labour supporters (37%).
The poll question is predicated upon the assertion that an independent Scotland "would need to adopt the euro".
Experts are divided over whether Scotland would be a joint successor state with the rest of the UK, inheriting its opt-outs from the euro and the Schengen passport-free travel area, or an accession state with the requirement to reapply.
No member state has ever separated so there is no precedent for it in EU law.
It is unclear whether the Scottish Government has taken its own legal advice as it has launched a court challenge against a request by the information watchdog to say whether it exists.
Today's poll carried out by YouGov suggests that more than three quarters (77%) of Scots think the SNP administration should reveal whether it has taken legal advice, including three-fifths of its own supporters.
Only 13% think the Scottish Government is right to withhold the information, rising to 28% amongst SNP supporters.
The Scottish Government insists disclosure would breach the Ministerial Code, which protects the confidentiality of legal advice unless there is a compelling public interest to release it.
Information Commissioner Rosemary Agnew has ruled that limited disclosure is in the public interest, and is preparing to defend her ruling in court in December.
Labour MEP Catherine Stihler, whose freedom of information request sparked the pending court battle, said the SNP is "out of touch with the people of Scotland".
"They think that the best way to run the country is to do it from underneath a shroud of secrecy," she said.
"They think that at a time of financial uncertainty, the best way to spend our money is by taking the Information Commissioner to court in order to allow important facts to be kept locked in Alex Salmond's desk in Bute House.
"This poll tells them, loud and clear, that the people of Scotland do not agree with them. They should listen to the voice of the people and release the advice that they have.
"We all know why Alex Salmond wants to keep this a secret.
"We know that his lawyers have told him that, despite what he has been telling the people of Scotland, if we separate from the UK, we will have to reapply to join the EU.
"This means that we would have to adopt the euro. It means border controls at the border with England and it means a massive financial hit to each and every family in Scotland."
Better Together said its assertion that Scotland would be a new member state is backed by current European Commission president Jose Manuel Barroso, former EC president Romani Prodi, former European fisheries commissioner Joe Borg, secretary general of the Convention on the Future of Europe Lord Kerr of Kinlochard, and EU law experts Dr Jo Murkens, Robert Hazell, Dr Lorand Bartels, Matthew Happold and Malcolm Chalmers.