Mrs May agreed but insisted her deal is a "good deal" and she wants the United Kingdom to leave with a good deal.
Labour MP Wes Streeting pressed Sir Keir to clarify if a proposal from colleagues Peter Kyle and Phil Wilson to back Mrs May's deal with the condition that it is then put to a confirmatory public vote is "wholeheartedly supported by the Labour leadership".
Warning MPs they faced "hard choices" after rejecting her deal for a second time, she said she would vote later to rule out a no-deal exit on 29 March.
May's predecessor, David Cameron, who held the European Union referendum in an effort to unite his party which has always been sharply divided over Europe, made a rare appearance and told Sky News: "I have always supported the Prime Minister in her attempts to have a close partnership deal with Europe and she continues to have my support".
Wordsworth's dancing daffodils do look golden in Downing Street but inside Number 10, where Britain's embattled Prime Minister is holed up nursing a sore throat after non-stop negotiations with Brussels over her Brexit deal, the mood is anything but sunny.
She said the Government will continue to work to leave the European Union with a "good deal", adding on Mr Corbyn: "He doesn't agree with Government policy, he doesn't even agree with Labour Party policy".
Mr Corbyn argued Mrs May has failed, no longer has the ability to lead, and must change her approach. It wasn't as bad as the 230 vote defeat on January 16 - the biggest in British parliamentary history - but still pretty devastating.
Hammond talks up United Kingdom economy despite Brexit 'cloud'
Speaking at the Institute for Government, OBR chairman Robert Chote said that even with a deal there could be further uncertainty relating to Brexit.
Labour wants no-deal to be "taken off the table" and is likely to back an amendment - a legislative tool - tabled by MPs Jack Dromey and Caroline Spelman ruling out the United Kingdom leaving without an agreement at any stage in the process.
As Mrs May said following the loss of yet another "Meaningful Vote", seeking an extension of Article 50 and therefore a delay of Brexit will now become government policy and all eyes will now turn to the European Union and whether they will in-fact grant this.
A cross-party amendment selected for consideration aims to "enable the House of Commons to find a way forward that can command majority support" on March 20, which could also start the process for "indicative votes".
"I believe we have a good deal".
Some of them believe it's time now to go hell-for-leather to leave without an overarching deal but move to make as much preparation as possible, and fast.
Today's votes saw three amendments debated and then voted on.
He referenced the official People's Vote campaign, who have said they do not back the proposal tabled by Independent MP Sarah Wollaston.