Labour leader Jeremy Corbyn and other party chiefs oppose the idea, saying Labour must honor voters' 2016 decision to leave.
While stopping short of an absolute commitment to vote down Mrs May's plans, he will tell delegates that it is highly unlikely any deal based on her Chequers blueprint could meet Labour's tests.
Mr Corbyn declined to say which way he would vote in any new in-or-out poll, while pointing out that he backed Remain in the 2016 referendum.
"Because some have said Labour could vote for any deal the Tories reach".
But shadow worldwide trade secretary Barry Gardiner said the idea that Mrs May might call another election was "Looney Tunes territory".
Ms Dodds replied: What we're saying is that we need at that stage if Theresa May can't command sufficient support in Parliament to get her deal though, we need to have a general election.
Starmer said the compromise reached at the Sunday night meeting - and which will be ratified by conference delegates on Tuesday - deliberately left open what the question would be.
The shadow chancellor had earlier enraged Remainers within the party by claiming that a People's Vote could be held without the option to stay in the European Union on the ballot.
These centrist MPs now find themselves on the sidelines and battling for their political lives in the face of aggressive attempts by Corbyn's supporters to de-select them, another issue that could raise tensions during conference.
Speaking on the fringes of the Labour conference in Liverpool, Rosie Duffield, the MP for Canterbury, said Labour should send anti-Semitic party members to Auschwitz to understand how poisonous their views are.
Andrew Adonis, a Labour member of the House of Lords who supports holding a second referendum, said Labour can't sit on the sidelines while the country staggers toward political and financial chaos. The first referendum is still keeping us busy. We want to be in control of that process.
John Mc Donnell is wary about rerunning the 2016 referendum
Meanwhile, sections of the crowd could be heard shouting: "Hey Jeremy, take a note, for the many, People's Vote".
"We will be arguing that it should be a vote on the deal itself".
His intervention prompted an angry backlash from pro-Remain Labour MPs.
Ms Butler's remarks were "far from what we should be standing for as a party", one Labour MP told the Press Association.
"The next leader of the Labour party has to be a woman."
They did not do this to be offered a farcical referendum on no deal or a bad deal. It absolutely must include the right to remain in the EU. He understood that the motion could allow Britain to vote to stay in the EU.
"Labour voters deserve to have their voices heard and be given a real choice on the Brexit deal".
Shadow equalities minister Ms Butler's comments were criticised by fellow Labour frontbencher Baroness Thornton.
Confirmation that the party will vote against the deal in the Commons leaves Tory whips facing an uphill battle to persuade Eurosceptic MPs to back it.
"But when Theresa May comes back with a supposed deal, we'll see what she comes back with, we'll put it against the tests we have advocated, the main test is about protecting jobs and the economy". No ifs, no buts. "And I think they should be sent there actually by the Labour party to see what people went through if they carry on repeating those things".
Brent crude falls to $82 per barrel
This comes after the US Congress has reconsidered legislation aimed at preventing OPEC from manipulating oil prices. He further said all producers - OPEC and non-OPEC - wanted to keep the price of oil at around $80 per barrel.
In as much as most movies show how gambling is bad or addictive, look on the brighter side, it is a good way of making money. With so many people shaming gambling, directors are trying to put it out there that it is not as bad as people make it seem.
Samsung shares hurt by negative Morgan Stanley forecast
The company will be starting construction soon on a special EUV facility as part of their Hwaseong complex in South Korea. The Note 8 has seen an incredible return to form for the company and saw over 4 million devices sold around the world.