After the SNP leader announced a renewed drive to break away from the UK, Labour and Liberal Democrat sources cast doubt on whether a campaign uniting the big Westminster parties is possible.
It raises the prospect that Ms Sturgeon may only face the kind of fragmented movement that tried and failed to prevent Brexit, with each political party attempting to make its own different arguments.
The stakes in the battle for the future of the UK were raised further on Tuesday when Ms Sturgeon pointed out that she has been elected on a clear manifesto commitment to Scottish independence, but that Conservative Prime Minister Theresa May “is not yet elected by anyone”.
Downing Street said on Tuesday that it is too early to say if a joint campaign to fight independence might be formed.
But a source close to Jeremy Corbyn said: “We’ve said in the past that was a failure, which is why we had our own campaign during the EU referendum.
“The leadership won’t think a campaign with the Tories is a good idea. But nothing has been decided yet because there is no referendum yet.”
While the Better Together campaign which united the Tories, Labour and Lib Dems against independence was accused at times of being too negative, it eventually won the referendum.
In particular, coordination between the parties allowed their leaders at the time to commit to what was called the “vow” to deliver change for Scotland.
While the referendum was won, Labour was devastated in the General Election that followed a year later losing almost every single Scottish seat it held to the SNP.
Party figures later admitted that appearing on a platform with the Tories during the referendum could have severely damaged Labour’s reputation north of the border.
A Liberal Democrat spokesman said: “Last time in the Indy Ref the Tories stumped up the money, Labour delivered the ground game and we delivered the Highlands.
“But that model really doesn’t look to be a starter this time around. Anything more than that we are going to have to wait and see.
“The ball is really in Labour’s court as to whether we work together or whether it goes like the EU campaign and they have their own separate thing going on.”
Announcing her intention to trigger a second referendum on Monday, Ms Sturgeon said the Westminster government had “not moved even inch in pursuit of compromise and agreement” with Holyrood over Brexit and even a good deal would be “significantly inferior” to the status quo.
In a taunting reminder that Ms May’s premiership is yet to be endorsed by the public at an election, the Scottish First Minister said she had the mandate to call a second referendum on independence.
A spokesman for Ms May later said that the Prime Minister wants to talk “constructively” with all parties in the UK on securing the “best deal” in Brexit talks.