Labour's polling numbers have remained relatively stable throughout the scandal, said Steven Fielding, professor at University of Nottingham, but the row continues to reverberate through the party.
"So if the parliamentarians, if spineless Tory MPs, lose the courage of their convictions and won't vote against whatever deal comes back, then my union and Labour's policy at the moment is to say, "well, if you are incapable of carrying out your functions in parliament, we should take the deal back to the people".
Earlier, Labour leader Jeremy Corbyn said he would back a second Brexit referendum if his Labour Party voted to pursue the move, heaping pressure on May, whose plans for a divorce deal with the European Union have hit an impasse.
Chants of "we are European" and flags bearing the slogan "not a done deal" were part of a huge protest in Liverpool to demand a final vote on the deal Theresa May strikes with Brussels.
Britain's opposition Labour Party kicked off its annual conference on Sunday hoping to take advantage of government turmoil, but separate rallies against Brexit and anti-Semitism brought into focus the obstacles in the way of power.
Prominent Labour MP David Lammy greeted the crowd from a stage set up outside the iconic Royal Liver Building, just metres from ACC Liverpool, where the Labour Party conference was getting underway.
Labour said in a statement that the current corporate governance structure which gives priority to shareholder interests over others was feeding a short-term corporate culture and holding back economic growth.
At Labour's annual conference in the northern city of Liverpool, Mr Corbyn, who in 1975 voted "No" to Britain's membership of the then European Community, said he would act on the result of a debate in Labour on a second Brexit vote.
The day in a picture Labour's deputy leader, Tom Watson, promotes the Labour Cycles initiative at conference.
Responding to claims that both wings of parliament are discussing an Autumn general election, Brexit Secretary Dominic Raab told the BBC's Andrew Marr programme the claims were "for the birds - it's not going to happen".
"Obviously I'm bound by the democracy of our party", Corbyn told the BBC.
In his interview with the Sunday Mirror, Mr Corbyn said: "I'm not calling for a second referendum".
"There will be a clear vote in the conference".
Melanie Crowley, a dyslexia support tutor, also from Birmingham, said: "I think people were conned into Brexit and it would be bad for the country".
At a public event at the conference, Labour MP Bridget Phillipson from Sunderland in England's north said despite nearly two-thirds of her electorate voting for Brexit she was campaigning for a "People's Vote".
Canterbury MP Rosie Duffield said she doubts people within the party would "still say and feel those same things" if they went to see the Nazi concentration camp in Poland.
He said: 'A new poll shows 86% of Labour party members want the British people to be given a final say on the UK's future relationship with Europe.
But Kinnock said Labour should not be put in the position where it could be accused of putting the party ahead of the country.