The U.K. has been told to come up with a so-called "backstop" solution for the Irish border as part of its divorce deal with the European Union so that no policed frontier emerges on the island after Brexit.
But Barnier said, "It is an all-weather backstop?"
The Prime Minister was "going to go into a phase where we are much more combative with Brussels", the Cabinet minister said.
Britain proposed a compromise solution for the Irish border issue on Thursday - a so-called "backstop" proposal - for a temporary customs arrangement that would keep Northern Ireland inside the EU's single market in goods for a temporary period.
An opinion poll for the BBC has shown surging support in Northern Ireland for a united Ireland. "What is feasible for a territory the size of Northern Ireland is not necessarily feasible for the whole United Kingdom".
And it calls for the arrangement to apply to the whole of Britain. "How does that fit with the absence of a hard border in all circumstances?"
"We look forward to the passage of the EU Withdrawal Bill next week and hope that, whether various amendments are passed or defeated, we will have a clearer picture of what happens next".
"Does the temporary nature of the customs arrangement mean that several adaptations will now be needed?" "We need regulatory alignment to avoid a hard border".
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Rather than setting a firm deadline for the end of the backstop, the document states: "The UK expects the future arrangement to be in place by the end of December 2021 at the latest".
In a coded warning to pro-EU Labour MPs, Starmer said there were "very divided views" in the party about a Norway-style model and he was "injecting some honesty about where we are in the party".
"Give us a straight choice between your deal on the best terms you can get or decide to stay in now we see the costs of leaving", said Mark Malloch Brown, the group's chairman, at an event in London.
The survey also found that 28 percent of respondents who previously wanted Northern Ireland to remain a part of Britain had changed their mind and now wanted to join with Ireland following the 2016 Brexit referendum.
"There needs to be more trust but there also needs to be more realism about what's possible and what is not possible", he added. Does it respect the integrity of the SM/CU (single market / customs union)?
"With the threat of a Cabinet resignation, Theresa May has signed up to a flawed proposal which is inconsistent with her earlier commitments", he said. On customs, Northern Ireland would form part of our customs territory.
It was not clear whether the European Union would accept the proposal.
A campaign funded by Hungarian-US billionaire George Soros on Friday published a "roadmap" for a second vote on Britain's European Union membership as confusion reigns over the country's post-Brexit relationship with the bloc.