There is a gap between what the Tory Remainer rebels think the prime minister promised them and what the Brexit Secretary David Davis thinks has been promised. "It is, however, irresponsible to proceed as we are".
He called for Brexit to be delayed, and for the public to get a second referendum on the terms of any exit deal.
Dr Lee, who represents the Leave-voting Bracknell seat, said in a lengthy resignation statement: "Our Parliament should be able to direct our Government to change course in our interests".
Speaking to reporters outside the meeting, Solicitor General Robert Buckland confirmed the Government was in discussions with rebels about establishing a fresh amendment committing to seek a customs arrangement - not a union - with the EU.
As time ticks by, May can no longer kick decisions down the road, increasingly under pressure from European Union negotiators to come up with detailed positions not only on customs, but also on future trade relations and governance.
Although these terms would not necessarily keep the United Kingdom in the customs union, defeat in the Commons would be politically explosive, as it would show May has no majority for one of her key "red lines".
The Bill will return to the Lords on June 18, kicking off a process of "parliamentary ping-pong" which sees it bounce from House to House until agreement is reached.
It is expected that Tuesday will see MPs decide whether Parliament should have the power to set the Government's negotiating goals if Theresa May's deal with Brussels is voted down.
But if the amendments being debated in Parliament this week force a change to the government's negotiating strategy, the wound could yet reopen. The Daily Express featured the British flag as its front page with the headline: "Ignore the will of the people at your peril".
The Sun had a frontpage of British icons including Stonehenge, a fish and chip shop, a London bus and a football, saying "Great Britain or Great Betrayal".
Phillip Lee, who resigned this morning, gave an impassioned speech from the "naughty corner" on the backbenches - flanked by Remainers including Bob Neill, Nicky Morgan, receiving congratulations for his decision by Soubry and Sarah Wollaston.
After it was not clear whether that would win over potential rebels, a minister offered Grieve a compromise to discuss parts of his amendment that the government could adopt - a move aimed at warding off a potential rebellion led by the lawmaker. But May is facing a potential rebellion from some Conservative lawmakers who want to retain close ties with the bloc after the United Kingdom leaves in March 2019. May's preferred approach is temporarily keeping the U.K.in some form of temporary customs union with the E.U., but this is unacceptable to hardline Brexiteers in her party.
On Tuesday, parliament will also debate other amendments, including a challenge to the government's plan to put March 29, 2019, or "Brexit Day", into law and an attempt to toughen a commitment to ensure a frictionless border between Northern Ireland and the neighbouring Irish Republic, which will remain in the EU. The text needs to honor her pledge to pro-EU Tories that she'll take account of their concerns over the possibility of leaving the bloc without a deal.