Business Secretary Mr Clark was challenged about the potential revolt on the Taxation (Cross-border Trade) Bill, often referred to as the customs bill.
But Mrs May faces further danger today with pro-EU Tories tabling amendments to the Trade Bill, which returns to the Commons.
The prime minister's office defended the government's decision, saying that it was still consistent with the previous government policy. That was promptly undermined by the resignations of her Brexit secretary, David Davis, and foreign secretary, Boris Johnson.
He tweeted: "I can't possibly go along with that and I don't see how anyone else could at this critical time with the clock ticking on #Brexit; it would be shameful even to consider it".
May now faces rebellion from the pro-EU flank of her Conservative party, who are outraged by her caving in to these harder Brexiteer demands. "Indeed, there is little doubt that if there was a second referendum and its result didn't suit Ms Greening and her remainer cabal, they would want a third referendum".
As MPs started several days of debates on Brexit legislation measures, Downing Street confirmed it was accepting four amendments. related to the proposed working relationship between Britain and the EU.
Where the government might struggle is explaining its acceptance of the demand that the European Union must collect tariffs on Britain's behalf, if London is to do the same - a suggestion one expert said the bloc's negotiators were unlikely to accept.
May claims that the trade bill will enable Britain to maintain the 40-odd trade agreements that the European Union has with countries around the world.
Veteran actress Rita Bhaduri passes away at 62
What's going to happen to her character? I was constantly trying her phone for the last 5 days but there was no response. But it was actor Zarina Wahab 's heart-breaking tribute for her FTII batchmate that deserves special mention.
"We believe the amendment is entirely consistent with what was agreed in December - we want a soft border with the Irish Republic but also have unfettered access to the United Kingdom single market", he said.
Jacob Rees-Mogg, the chairman of the ERG, told the BBC "we'll have an idea of the numbers at 10pm on Monday evening" while one ERG insider added that they were "intensely relaxed" about the number of rebels they had signed up. "That would be damaging to our "no deal" preparations".
Key New Labour figures have also come forward in criticising the prime minister, with former leader Tony Blair branding the proposals "just mush".
"I do not understand why people thinks this lacks democratic legitimacy".
Labour shadow chancellor John McDonnell said such a vote, listed for Tuesday evening, shows the Government is in "chaos".
His resignation was seen by many as a risky sign for May, who is now facing potential unrest from both sides of her party.
Johnson, warned Monday that the Brexit "dream is dying" and Britain is "headed for the status of colony" with May's plan to stay close to the EU.
But, fueled by criticism from US President Donald Trump and anger at grassroots level in the party, the sentiment against May has gained fresh momentum.