''Would I join Team Scotland [in the event of a Yes vote]? If I were asked to do whatever I could to make that new Scotland work, I would do it"'

"It wouldn't be a good result," she says. "I want it to be more than that. If only 51% of the people of the country feel the same way as me, on something I feel so strongly about, then of course I would be disappointed."

We meet two days after a YouGov poll revealed an increasing number of Labour voters are backing independence. Why, does she feel, some of her party's own supporters are shifting? "I'm not sure if it is an increasing number," she says, speaking in Labour's Glasgow headquarters. "People are weighing up the arguments, back and forward. The warmth of the No vote is strong, but I also recognise there is an attraction in this argument for people. People don't like the Tory Party, don't like what's happening in their country and are being promised the possibility of change."

I paint a picture of a Labour voter who has been on low pay and not had a kick of the ball from successive governments. What has this person got to lose by voting Yes?

"They could lose a lot if you have a £6 billion black hole," she responds. "I would probably say to them as well, look at what the SNP have done for low-paid workers like you. We put through measures to increase the living wage for people in jobs from public procurement and the SNP Government voted them down."

Lamont, 57, did not enter politics to discuss the constitution. Even after becoming her party's leader in 2011, the debate on Holyrood's powers is said to have left her cold.

However, if there is a Yes vote, there will be a call for senior politicians to join "Team Scotland" and negotiate a constitutional settlement with the rest of the UK. Would she accept such an invitation?

"I'd always step up to the mark to serve the people of the country. If I were asked to do whatever I could to make that new Scotland work, I would do it."

Just to be clear, does that mean she would accept a role in Team Scotland? "Yes."

She would also like a firm commitment from the Yes side on the implications of voters backing the Union. The First Minister has said a No vote would kill independence for a "generation", but Lamont believes it should be more definitive.

"I think that should be it, full stop," she says, meaning independence should never come back.

She is candid on the post-vote aftermath, but rumours swirl the Labour floor at Holyrood about Lamont's future.

Senior sources have said Lamont is not enjoying leading Labour and could quit after September.

It is assumed any vacancy would be of interest to MPs Anas Sarwar, Jim Murphy and MSP Kez Dugdale, the latter of whom is a Lamont favourite. I ask whether she will absolutely, categorically, lead Labour into the 2016 Holyrood election.

"Unless I am in my box," she says. "Apart from that, absolutely."

She explains: "There's a natural break for Scottish politics come September 18. If I got to the point where I thought, 'I don't really want to do this, I've done it for two-and-a-half years, I've done the best for my party, let's stop now', that would be the time I would do it, but that's not what I feel."

It is said she and Murphy, who has nearly completed his referendum tour of 100 Scottish towns, have an uneasy relationship.

Would she welcome Murphy standing for Holyrood in 2016?

"Absolutely," she says. "He's been a source of great advice to me."

Does she think he is a potential Scottish Labour leader?

"He's a very talented man, full of energy," she says, before adding a telling caveat. "Like many more [of] our young generation coming through in the Parliament. There are loads I think are going to make their mark, too."

One of the contributions that has defined Lamont's leadership was her "something for nothing" speech in 2012, where she critiqued some universal benefits. Looking back, does she regret the phrase?

"People have said it was a 'something for nothing culture', that's not what it is. It's only in Scotland you could think we could get something for nothing, that it doesn't cost us anything anywhere else in the system."

In this regard, does she think the council tax freeze is progressive?

"No," she replies. "We need to find a way of having a conversation across the parties on how you fund local government."

Does she support graduates paying tuition fees? "I think we have to look at these things," she says.

The interview moves to Lamont's deputy Anas Sarwar, who has irked some of his colleagues by sending his son to a private school. Given that Labour runs Glasgow's schools, what did she make of the snub?

"I'm not going to run a commentary on the reasons why he has made that decision," she says. "I made a different decision to send my children to the local state school."

Is he not a hypocrite? "I don't want to comment on what his individual decision is."

Did you consider, even for a second, sending your own children to a private school? "No."

Back on the referendum, I sense Lamont grasps how high the stakes are for Scottish Labour.

If the country votes No, the SNP could spend the next year engaged in civil war; if there is a Yes, her own party may never recover.

On September 19, Labour will either have a chance of seizing power at Holyrood at the next election, or be staring into a bleak and uncertain future.