He added: "At some point there will be a reckoning: either with a cobbled-together Brexit deal or if the negotiations fail".
"The first thing I want to understand is why this has been rejected?"
The pound traded higher against the euro and the dollar after the votes. They can not be trusted with Brexit.
Several pro-EU MPs threatened to rebel over whether parliament should have more control over any final deal agreed with the EU in Brussels.
Tom Tugendhat, Conservative chairman of the United Kingdom parliamentary foreign affairs select committee, said there would be a "new government" if Mrs May lost the so-called "meaningful vote" on the terms of withdrawal, due to take place in October.
That was the frank message from Tory MP Mike Wood, who has warned his fellow politicians that people are sick and exhausted of them bickering amongst themselves over the UK's departure from the EU.
"The meaningful vote is going to be either the government's deal is accepted in which case that is the meaningful vote to accept it or it isn't accepted, in which case frankly there is going to be a new government", he told "Sky News".
A United Kingdom government's compromise to avoid a Commons defeat on Brexit has been rejected as "unacceptable" by leading rebel Dominic Grieve. It was sealed at a private meeting between May and potential rebels.
MPs will debate amendments to the EU Withdrawal Bill on Wednesday, with the threat of defeat on a "meaningful vote" clause which would force the government to gain Parliament's approval before leaving the EU without a deal.
The latest confrontation took place in the unelected House of Lords, which on Monday voted 354 to 235 in favour of a plan that would allow parliament to shape the government's next steps in the event that MPs reject the deal May negotiates with Brussels, or if she fails to negotiate one at all.
The Labour Party's Chuka Umunna, who backed staying in the European Union, welcomed the concession as the end of the government threatening to allow Britain to crash out of the European Union without a deal.
But her parliamentary problems will not stop there.
The rebels are holding out for more, warning that they could bring down the government.
There is little May can do.
The EU is expecting her to have made progress by a summit in June and both sides want to reach a deal by October.
Lee said he had had "conversations with ministers at all levels who are concerned about the direction of travel".
Labour's Brexit policy chief, Keir Starmer, said May had been forced to avoid a "humiliating defeat" and "to enter negotiations with her backbenchers".