She admitted there had been "a debate" about what a "meaningful" vote for Parliament meant: "I've listened carefully to the concerns, I've put an amendment down which I think balances this issue of the role of Parliament together with the need for us to ensure we don't overturn the decision of the British people".
May today said: "I listened to their concerns and I undertook to listen to their concerns".
He told BBC One's Sunday Politics: "And I can assure you I wake up at 2am in a cold sweat thinking about the problems that we have put on our shoulders".
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.
Tory rebels want Parliament to be able to direct the government's course at such a potentially "apocalyptic moment".
"The Government's position has not moved since last year's white paper, and even Labour's manifesto was quite clear that free movement of people is not consistent with Brexit, and that we must have the freedom to conclude global trade deals. The difficulty is that the Brexit process is inherently risky". Other rebels suggested the prime minister had "caved in" to the demands of Brexiteers. "I've done exactly that".
Robert Buckland, the Solicitor General, insisted United Kingdom ministers intended to press on with their own meaningful vote amendment, which suggested a Government motion on the final deal could not be amended; rebels believe this means the meaningful vote would, therefore, not be meaningful.
"Most people in the Black Country want us to get on with negotiating the best deal for Britain with the European Union", he added.
Mexico Fans' World Cup Goal Celebration Causes 'Artificial Earthquake'
At the end, their fans, largely dotted around the end where they scored their goal , hugged each other in delight and relief. He played his last two club seasons with Mexican team Atlas, where he started his professional career in 1996.
The Prime Minister has insisted she did not break her word on Parliament having a meaningful vote on final decisions about Brexit, but argued that MPs can not expect to "tie the hands of Government in negotiations".
"That must be wrong and Parliament in those circumstances will have to take action to try to remedy it without causing too great a political crisis - it will certainly be quite a big political crisis", he insisted.
"Theresa May's plans are nothing if not breathtaking in their arrogance and deceit", said Dick Newby, their leader in the Lords. It was clear she couldn't keep both promises - we are now finding out which lie she was telling.
Mr Grieve told the Press Association that his comments about collapsing the Government referred to a future vote on rejecting a Brexit deal, not to this week's clash with the PM. "This is simply unacceptable", he declared. Calls for MPS to have a "meaningful vote" on Brexit are nothing to do with parliamentary scrutiny; they are about stopping Brexit.
"The Conservatives are making a complete mess of Brexit".
Also on the Brexit agenda for Parliament on Tuesday is the expected appearance of Arron Banks, the businessman who financed one of the pro-Brexit campaigns during the 2016 referendum.
"Ultimately, this saga demonstrates that the Tories are more interested in party unity than the country".