He added: "This format would also not suitably represent either the support for Remain across the whole of the United Kingdom, or the growing public and political support - including from the SNP, the Greens, the Liberal Democrats, Plaid Cymru and an increasing number of members of both the Labour Party and the Conservatives - for a second referendum in which the option of remaining in the European Union could be put to the people".
There's every sign they won't, and that would leave May with a set of unpalatable options that range from taking Britain out of the bloc without a deal - with potentially disastrous economic consequences - to holding a second referendum.
Asked about the situation back in the UK, Mrs May said: "The next nine days are a really important time for our country leading up to the vote on this deal".
The PM said a defeat in the Commons in would mean "there will be decisions to be taken by Government and by business in relation to the practical preparations they would be looking to make for no-deal".
MPs will vote on Prime Minister Theresa May's Brexit deal in the Commons in two weeks, but with staunch cross-party opposition persisting, the PM may well see her deal voted down. May's office says she hasn't sought a bilateral meeting with him.
When the Japanese PM publicly calls on May for "support to avoid no deal" - as he did today here in Argentina - because of the damage trade friction at the border would do to important Japanese companies with big factories in the United Kingdom, it is very hard for the PM to plausibly argue that she would simply let chaotic events drive the United Kingdom to the cliff edge of an unnegotiated withdrawal from the EU.
The group of Scottish parties is to propose a single motion against the EU Withdrawal Agreement.More news: Australia's David Pocock out of England clash with neck injury
"Sadly, what we see from the Labour Party (is) their various attempts to frustrate Brexit and frustrate this vote", May told the BBC. People need to have some clarity about that...
"The bottom line is that we must not end up with a no deal by default".
Gyimah, who backed remaining in the European Union during Britain's 2016 referendum, said the agreement was "a deal in name only". "It says we will be able to do those trade deals, and we will be able to do them with the U.S. and others".
May has faced questions as to why she is spending time selling her deal to the public rather than the lawmakers who will vote on it.
Hardline Tory Brexiteers may have failed to muster the sending of enough letters of no confidence in the Prime Minister to backbench supremo Sir Graham Brady a fortnight ago and trigger a leadership battle.
Scottish council umbrella body Cosla has given its support to calls for a second referendum on the Brexit deal and the possibility of remaining in the EU.
But hinting at potential further resignations from Mrs May's top team over Brexit, he added: "Members of the Cabinet who don't vote for the deal won't be members of the Cabinet".