"Barnier can bluster, Vardkar and Coveney can foot stamp all they like, but the fact remains that the prime minister has now got the support of whole of parliament in opposing their demands that Northern Ireland would stay in the single market and customs union", he said.
She said Labour was in an "even greater mess" than the Conservatives, with the 'old Trotskyists in charge.
"Problem is, I don't think she's in charge any more".
Highlighting the fine margins May is dealing with, Tuesday's victory required the votes of four pro-Brexit Labour opposition lawmakers who backed the government in defiance of their party's instructions.
Since the Brexit referendum, all parties have urged the party to forgo its long-standing abstention policy to take its seats and vote on Brexit legislation to benefit the country.
Furious Remainers rebelled to back an amendment to force the Prime Minister to try to keep the United Kingdom in a customs union with the European Union after Brexit.
One of the amendments practically says that the United Kingdom should not be collecting tariffs for Brussels unless the European Union does the same for Britain, one of the key ideas in May's original Brexit white paper that was created to keep the Irish border invisible.
In one of her most challenging days as a PM, the Tory leader on Thursday night just narrowly managed to scrape through a crunch parliamentary vote on her customs plan - which would see the United Kingdom leaving the EU customs union.
Ministers argued the amendment would put "massive restrictions" on its ability to forge "an independent trade policy" after Britain leaves the European Union next March.
This week's votes "showed that the hard Brexit Conservatives have the numbers to sway the government's Brexit strategy, in contrast to the Rebel Remainers who have lost or withdrawan some of their key amendments".
Glyn Davies, MP for Montgomeryshire, said one of these amendments, passed by just three votes, meant the deal was now likely to be rejected by the EU.
Last month, Carwyn Jones gave a speech in London aimed at the prime minister - change tack or the United Kingdom faces the "very real possibility of a catastrophic no-deal Brexit", he said. It was then undermined by the resignations of her Brexit minister David Davis and foreign secretary Boris Johnson. The commission said Grimes and an official from Vote Leave have both been referred to police "in relation to false declarations of campaign spending".
"It's not evident, or not obvious, that the government of Britain has the majority for any form of Brexit quite frankly", he said.
Mrs May was invited to visit the border by DUP leader Arlene Foster when she held talks with the Prime Minister at No.10 a fortnight ago. Labour has previously abstained on some Brexit legislation votes, but ahead of Monday's vote on the European Union tariffs amendment changed its vote to one of opposing the hard-Brexit amendment.