Conservative lawmaker Phillip Lee resigned as a justice minister Tuesday so he could speak out against the policy on Brexit.
"If, in the future, I am to look my children in the eye and honestly say that I did my best for them I can not, in all good conscience, support how our country's current exit from the European Union looks set to be delivered", he said.
The minister also showed a united front with the Prime Minister by denying reports he came close to resigning.
In Westminster, a government fearing defeat in the Commons made concessions to rebel Tory MPs to give the house more of a veto than it's ever had over Brexit negotiations.
"A vote between bad and worse is not a meaningful vote".
"Secondly, we can not change the fundamental constitutional structure which makes the Government responsible for worldwide relations and global treaties".
A Downing Street source said: "We will get a good Brexit deal that works for everybody in the UK".
Speaking on Channel 4 News, Mr Rees-Mogg delivered his first reaction to the votes on the Brexit Lords amendments that took place in Parliament today.
But pro-EU Tory MP Heidi Allen warned that other members of the Government may follow Dr Lee out of the door.
The bill underpins the government's Brexit strategy.
Ministers have told rebel Conservatives they will agree to seek House of Commons approval for their course of action if no political agreement has been reached on the Withdrawal Agreement agreed with Brussels by November 30, which the original amendment had demanded. Brexit-backers objected as it would have all but removed the no-deal nuclear option from negotiators' arsenal.
Grieve told MPs: "If we don't achieve a deal at all, the fact is we are going to be facing an enormous crisis".
Former Attorney General Dominic Grieve had been a repeat rebel in previous debates, but he voted with the government after "personal assurances" from Theresa May - because he is "quite satisfied" MPs will end up with a meaningful vote anyway. Currently, the government is offering lawmakers a "take it or leave it" vote on the final deal.
A dispute quickly arose about the third clause of Grieve's amendment, with Brexiters, including some ministers, quickly saying all that had been agreed was talks - and no government could agree to be "directed" by MPs.
The government says lawmakers should be offered a choice only between its final deal and no deal at all.
"Where some of its most senior people who hold the greatest offices of state, at every twist and turn, when our Prime Minister moves towards securing a Brexit that will serve everybody in our country, the softest, most sensible Brexit, both publicly and privately they undermine her and scupper her attempts".
However, the compromise is only likely to delay a full-blown showdown on the customs union until trade legislation returns to the Commons in July.