May also told them she would try to capture another of their concerns, as enshrined in Grieve's amendment to the EU Withdrawal bill - which would much more explicitly give MPs the whip hand in Brexit talks, if May has still not done a deal with the EU by February next year.
Phillip Lee's resignation came hours before British Prime Minister Theresa May faces crunch votes in parliament and a potential showdown with pro-EU rebels in her ruling party.
The debate, which lasted for almost three hours, was split down the usual non-partisan lines that have emerged as a result of Brexit, with the likes of Labour's Kate Hoey and John Mann saying they would back the Conservative government, while Tories including Ken Clarke and Anna Soubry spoke in favour of Grieve.
In a concession, the government promised that lawmakers would have a say on what to do next if there is no agreement with the European Union, or if Parliament rejects the deal offered.
The Lords amendment on a "meaningful vote" for MPs was defeated in the Commons by 324 to 298.
Ministers have conceded in principle to Tory rebels" demands for a "meaningful vote' on the eventual Brexit deal.
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.
Brexit protesters outside Parliament House.
But if the amendments being debated in Parliament this week force a change to the government's negotiating strategy, the wound could yet reopen.
Parliamentary debates about complex legal amendments rarely rouse much heat, but passions run high over anything to do with Brexit.
Opposition Labour lawmaker Chuka Umunna had earlier accused Britain's tabloids of intimidation, holding up Tuesday's edition of the eurosceptic Daily Express.
It featured a British flag and the headline: "Ignore the will of the people at your peril".
Conservative MP Sarah Wollaston said on Monday morning she was "minded" to defy party orders and back the meaningful vote amendment.
A spokesperson for the Department for Exiting the European Union said: "On the meaningful vote we have agreed to look for a compromise when this goes back to the Lords".
They have an ace up their sleeve as they go into talks with the government: if May reneges on her pledge, pro-EU members of the House of Lords will amend her legislation again.
'The objective of the EU Withdrawal Bill is simple - it is putting EU legislation into law to ensure a smooth and orderly transition as we leave, ' she is expected to tell them.
"Parliament, don't stand against the people - implement their will!"