Last month, Rees-Mogg said: "The payment of money has to be conditional on a free-trade deal and the agreement must say that".
"This requires a legally operative backstop, an all weather insurance policy, to address the issues of Ireland and Northern Ireland".
He also said that workarounds with respect to the Northern Irish border could not result in any "additional bureaucracy" - an apparently brand new requirement it will be virtually impossible to fulfill.
"This is what we're working for but, of course, we need to be prepared for all eventualities".
He indicated the European Union was ready to amend its "backstop" proposals for the Irish border, which have become the biggest stumbling block in talks.
Barnier said the backstop arrangement in the final agreement will "not necessarily be ours" but he insists there must be one.
"We need to find the right place and right time to carry out checks to protect consumers and to protect the single market", he said. Only time will tell.
Instead, May said the European Union must engage with her Brexit "white paper" policy document released earlier this month, which proposes negotiating the closest possible links for trade in goods to protect businesses and to fulfil a commitment to avoid having infrastructure on the border.
The EU gave a lukewarm welcome to the paper.
He also insisted that the responsibility for resolving any outstanding issues rested with the British, since they were the ones who chose to leave - and that they would have to be resolved probably by December, as the process of ratifying any withdrawal agreement in the European Council, European Parliament, and British Parliament would not allow for negotiations to carry on to March 2019, when Brexit is supposed to happen - on paper, at least.
Barnier questioned some other key aspects in the white paper, as well as the Irish border.
The EU has long complained that May has delayed the Brexit negotiations because internal bickering within her Conservative Party has brought her government to the brink of chaos. He has let the cat out of the bag by acknowledging British firms could be more competitive.
Many Brexit or "Leave" campaigners feel they are losing ground to voices questioning the meaning of the 2016 vote.
"As I told the ministers, there are several elements in this white paper that open the way to a constructive discussion regarding the political declaration on our future relationship", Barnier told a news conference in Brussels following a meeting of European Union ministers.
The extent of Mrs May's reassurance to unionism may also be linked to next week's first meeting of the British-Irish Intergovernmental Conference for more than a decade - a meeting about which some unionists have been nervous.
The EU is painfully aware that it is questionable if May could master a majority for any withdrawal agreement in the United Kingdom parliament, and also acknowledge that the proposals in the white paper do not reflect the EU's red lines. "If indeed we have no deal on anything life as we understand it in this country is going to grind to a halt".
Brexit Secretary Dominic Raab said a deal could be done if both showed "energy, ambition and pragmatism".