"If we can't get a general election, we've kept the option of People's Vote on the table and that's what we'll go for, but I'd much prefer a general election".
Shadow Chancellor McDonnell, a key ally of Jeremy Corbyn, indicated today that any new referendum should be on whether to accept a deal with Brussels or to conduct fresh talks with the European Union, not on trying to reverse the 2016 Brexit vote.
Mr Watson told The Observer: "Jeremy and I were elected in 2015 to give the Labour Party back to its members".
"The motion before the Labour conference doesn't rule out a second referendum", Brendan Chilton, general secretary of the Labour Leave campaign, told Reuters.
Mr McDonnell later sought to quash speculation about rifts at the top of the party, telling a conference fringe meeting that "Keir is right" to say that all options were on the table.
Labour leader Jeremy Corbyn said over the weekend that he would shift his weight behind a decision to stage another Brexit referendum, should his party demonstrate clear support for the move.
"Certainly, there was no ruling out of anything, and no ruling out of remain as an option".
Shadow Chancellor John McDonnell said Jeremy Corbyn should be succeeded by a woman.
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David Lammy said "millions" of people had been campaigning for another vote.
'If the people's party decide they want the people to have a final say on the deal, we have to respect the view of our members and we will go out and argue for it'.
The 'six tests' comprise a series of metrics put forward by Labour's Brexit shadow minister, Sir Keir Starmer, that provide the party with a framework by which to judge their support for Theresa May's plans.
But the Shadow Chancellor also stressed: "The issue there is that we're saying "respect the last referendum" and I just think we have to be careful what we wish for".
"If the government is confident in negotiating a deal that working people, our economy and communities will benefit from, they should not be afraid to put that deal to the public".
"But we will push, if Theresa May fails, we will push for a general election because that's the choice that people should have". It calls for Britain to leave the EU but remain in the bloc's customs union with "full access" to the EU's huge single market.
With Tuesday the day for the vote on the second referendum motion, the Labour leadership will work hard to try to mute the squabbling - keen to push on with economic announcements they hope will tap into growing discontentment in Britain.
Liverpool is a Labour heartland and voted overwhelming for Corbyn's part in the general election past year.
Labour backed the "remain" side during the 2016 referendum but Corbyn's support was lukewarm.