Prime minister May also told reporters in NY on Tuesday that an election before Britain leaves the European Union would "not be in the national interest". In the United Kingdom that means a vote by lawmakers, and the math looks ominous for May's minority government.
She said it was not impossible Labour would vote to support a deal made by the Prime Minister, but added "we are a long way away" from anything the party could back being produced.
Labour shadow Brexit secretary Keir Starmer opens a debate on Brexit during the Labour Party's annual conference.
Corbyn's answer is that May should call a general election, in the hope that Labour wins power and then negotiates an exit deal that he said would better protect jobs, trade and workers' rights.
If Labour rejected May's deal, the weakened prime minister would need the backing of nearly all her Conservative MPs to get over the line, which seems unlikely given her own party's ideological splits.
Delegates at the party's conference in Liverpool are expected to back a plan that could lead to a fresh public vote which could include the option of ditching Brexit altogether.
Labour's position leaves the prime minister brutally exposed to a rebellion by restive Tory backbenchers, with fewer than a dozen able to fracture her fragile control of the Commons in the upcoming vote.
She will go on to say she has a plan for an economy that is "knowledge-rich, highly-innovative, highly-skilled and high quality but with low tax and smart regulation".
But there have been reports that some within her administration believe a fresh poll could give her the comfortable majority she needs to drive through a Brexit deal in the face of increasingly robust opposition from both the Leave and Remain wings of her party.
Sir Keir released an analysis of the Brexit blueprint agreed by the Cabinet at Mrs May's country residence, which he said showed it failed to pass Labour's six tests.
Mr Gardiner instead praised Labour leader Jeremy Corbyn for striking a conciliatory tone with the European Union, and vowing to compromise over key issues in a bid to secure a viable Brexit deal.
Barnier himself tweeted on Wednesday that he was "working for an orderly Brexit" - Brussels-speak for averting a collapse of talks that could see Britain, and European Union businesses and citizens, plunged into legal limbo on Brexit Day next 29 March.
The party's finance spokesman, John McDonnell, said any such vote should be on how - not whether - to leave the EU.
"It is true that we have got more people employed than ever before, and a million people now doing apprenticeships".
"Of course, to a significant extent, this also depends on what Britain really wants - the discussion isn't so clear here", she said.