May has committed to triggering Article 50 by the end of March.
It had been predicted that she might do it as soon as Tuesday, so that the EU-27 could get together before the Easter break and agree on the guidelines for the negotiations. That vote was won by 331 votes to 226.
"This will be a defining moment for our whole country as we begin to forge a new relationship with Europe and a new role for ourselves in the world", she said while addressing members of parliament (MPs) in the House of Commons.
Mr Verhofstadt said: "Since I've been appointed as the European Parliament's Brexit negotiator, I have also received numerous testimonies and letters of support from British people anxious about their future".
Theresa May ordered her party to overturn these amendments in the House of Commons on Monday night, easily defeating opposition from Labour and Liberal Democrat MPs.
He also insisted that the government's hands should not be tied before negotiations start.
In a letter to The Times, which is signed by Louise Richardson, the Oxford vice-chancellor, and the heads of all but three of the colleges, the academics dismiss as insufficient the indications by ministers that European citizens already resident in Britain were likely to be allowed to stay.
While this is now looking less likely, ministers insist that Brexit will begin by the end of March, putting Britain on course to become the first country to leave the European Union by March 2019.
Although June 20 - nearly exactly a year since the U.K.'s Brexit referendum - has been penciled in, the bloc hasn't ruled out governments having the opportunity to give approval at a scheduled gathering on May 16 or at an extraordinary meeting should the paperwork be completed in time. "A "no deal" scenario would open a Pandora's Box of economic consequences", said Paul Drechsler, president of the Confederation of British Industry, in a recent speech in London.
Barnier and Britain must also work out practical issues such as what language the talks will be held in - Barnier is French - and the timetable, though some of those issues may be sorted out earlier.
"Now, it's time to go into these negotiations with some ambition and support the government, so it can secure the very best deal - one that is good for the whole United Kingdom, and good for the European Union too", Tory MP and former minister Dominic Raab said.
Back it went to the House of Commons who will make a decision on those amendments, and then it's back to the Lords again.
It is expected in late May to early June - almost a year after Britain's referendum vote to leave the bloc.