Jo Johnson urged the Prime Minister to let the Commons vote on her Brexit deal next week as he expressed concern at the way Downing Street is treating Parliament.
Asked if Cabinet had talked about the issue, Mr Hinds told Sky News: "No. Government policy couldn't be clearer".
Mr Juncker said he had been able to convince her that his remarks had referred to the wider Brexit debate in the United Kingdom, joking: "After having checked what I said yesterday night, she was kissing me".
"There is nothing inherently undemocratic about asking the question again if parliament can't resolve it - and Parliament can't resolve it because we have a hung parliament".
With just over 100 days until Britain leaves the bloc on March 29, Brexit remains up in the air with growing calls for a no-deal exit, a potentially disorderly divorce that business fears would be highly damaging, or for a second referendum.
"If MPs (lawmakers) dig in against the prime minister's deal and then hunker down in their different corners, none with a majority, the country will face serious trouble". He did not directly address the suggestion he had talked up the prospect of another vote.
"I have to say, personally, I wouldn't have a huge problem with Parliament as a whole having a say on what the options were".
However there was no disguising the disappointment on the British side that Mrs May came away from the two-day summit in the Belgium capital with only limited assurances regarding the backstop, which is intended ensure there is no return of a hard border on the island of Ireland. It is not going to happen this week.
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During her meeting in Brussels, Mrs May said she had to be able to convince MPs that the United Kingdom would not find itself tied to the European Union indefinitely through the "backstop".
He is under pressure to launch a confidence vote in the government in the Commons, but has held off so far because he believes May would win. "I don't think the European Union could be remotely sure that if we don't find a way through this we wouldn't end up with no deal".
Speaking at the Leave Means Leave rally on Friday, the former Ukip leader said: "My message, folks, tonight is, as much as I don't want a second referendum, it would be wrong of us on a Leave Means Leave platform not to get ready, not to be prepared for a worst-case scenario".
"They have been working away like rodents in the basement for years trying to nibble away at the foundations of our relationship with Europe".
May's criticism of the former Labour prime minister was striking for its anger.
Mrs May said: "For Tony Blair to go to Brussels and seek to undermine our negotiations by advocating for a second referendum is an insult to the office he once held and the people he once served".
"Far from being anti-democratic it would be the opposite, as indeed many senior figures in her party from past and present have been saying", he said.
"What is irresponsible, however, is to try to steamroller MPs into accepting a deal they genuinely think is a bad one with the threat that if they do not fall into line, the Government will have the country crash out without a deal".