The messages, received by "The Sunday Times" involve Steve Baker, the deputy chairman of the Conservative Party's 100-strong hard-Brexit European Research Group (ERG), telling colleagues that May's Brexit negotiations with Brussels were a "complete waste of time".
May thanked MPs who supported the government in Thursday's Commons vote despite rejecting the withdrawal agreement last month, saying they had shown a "determination to find a way forward for our country".
In his talks with the leaders of the EU member States and the President of the European Commission may plans to find a solution to the border problem with the Republic of Ireland (backstop), which is one of the biggest problems Brexit.
'The question is, given those worries how would European countries explain to their electorates that there was a proposal from Britain to get agreement, by altering the backstop, which was then rejected on ideological grounds, when the outcome of that could be that you saw recession spreading to the people of Europe?'
"Instead, our party can do what it has done so often in the past: move beyond what divides us and come together behind what unites us; sacrifice if necessary our own personal preferences in the higher service of the national interest; and rise to the level of events in a way that restores the faith of the British people in our political process".
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"I don't think it's the mechanism that matters, it's the objective", he told the BBC's Andrew Marr.
"While the commission engaged seriously with these proposals it expressed concerns about their viability to resolve the backstop", a DExEU spokesman said.
British Prime Minister Theresa May on Sunday called on members of her Conservative party to 'move beyond what divides us, ' three days after she suffered another humiliating defeat on her Brexit plans in parliament.
May's office did not give a date for the Juncker talks.
"Time is a luxury we no longer have, so people are bracing themselves for the immediate potential impacts".
The European Commission on Monday stepped up its "no-deal" outreach to EU businesses in the area of customs and indirect taxation such as Value-Added Tax, to prepare for a "no-deal" scenario when the United Kingdom is set to leave the EU on March 29.