The challenges to May's proposals came as some British politicians again questioned the legitimacy of the 2016 Brexit referendum, following an Electoral Commission finding that the official campaign for Brexit broke election laws.
On Monday, May gave in to Tory hardliners by accepting four amendments to the bill, underpinned by her Brexit white paper, meant to toughen up her negotiating stance.
Meanwhile, Mr Wilson felt the United Kingdom negotiating team was now in a "much better position" as a result of the amendments passed in the Commons on Monday, adding: "It shows Brussels that the PM has no more room to manoeuvre and they shouldn't expect any more concessions from her".
Although far from lavishing praise on the United Kingdom government's new Brexit plan, it's an interesting change of emphasis from a first minister who has to date exclusively fired his rhetorical arrows towards Downing Street. "Even with a net vote in favour of a hike, we are likely to see a one and done", Neil Jones, head of FX hedge fund sales at Mizuho Bank said.
The paper also proposes a new customs arrangement with Brussels, whereby the United Kingdom would collect tariffs on behalf of the European Union for goods ultimately going there.
The spokesman said that was met by the government's pursuit of "a mechanism for the remittance of relevant tariff revenues". In all, 42% said no, an increase of one point.
"This news makes the narrow referendum result look dodgier than ever", Labour lawmaker David Lammy said.
The battle over the amendments to the Taxation (Cross-border Trade) Bill, or customs bill, is unlikely to be the last that May and her team will have to face.
He unfavourably contrasted her Chequers blueprint - which envisages Britain signing up to European Union rules and regulations for goods (a "common rulebook") - with the PM's Lancaster House speech of January 2017.
"Labour is clear that a new comprehensive customs union with the EU after Brexit is the best way to protect jobs, the economy and to avoid a hard border in Northern Ireland".
On Monday, May infuriated Conservative lawmakers who want to keep the closest possible ties with the European Union when she chose to accept a number of demands by hardline pro-Brexit MPs from her party.
The commission said it found significant evidence that Vote Leave did this by funneling cash to a small, unregistered pro-Brexit youth group, BeLeave. "It's the worst of both worlds".
The mounting deadlock leaves no certainty that any outcome to Brexit negotiations this fall could command enough support for approval from Parliament later this year, something that could yet put the process on an unpredictable and perilous path.
But he says her government is "damaged" by giving in to what he calls a 'faction led by Jacob Rees-Mogg'.