"Higher unemployment, lower wages, higher prices in the shops - that is not what the British people voted for in June 2016", he said.
But Britain's attorney general, Geoffrey Cox, dealt a blow to May's plans, saying the assurances she had been given still meant the United kingdom could be locked in the bloc's orbit after Brexit, the most controversial issue for Brexit-supporting lawmakers.
The fatally-wounded Mrs May, who had originally put forward the proposal to block a no-deal on March 29, was forced into the extraordinary situation of voting against her own bill, after parliament led by Tory Remainers ambushed her by supporting an amendment to make the block permanent.
"I believe we have a good deal", May said.
"I think it is still alive, I do", Ms Truss told BBC Radio 4's PM.
The EU would prefer only a short extension, with the deadline of EU-wide parliamentary elections due May 24-26, although it is unclear that this would be long enough to solve the impasse in London.
The defeat on Tuesday clears the way for further votes in Parliament on Wednesday that could clear the way for a "no-deal" Brexit, which would end decades of European integration on March 29, or allow MPs to request a delay.
"The House has today provided a clear majority against leaving without a deal, " Mrs May, hoarse and exhausted, told parliament immediately after the vote.
She told lawmakers after their Wednesday vote they are down to two choices: approving a withdrawal agreement in coming days and requesting a short delay to Brexit, or requesting a "much longer" extension from the European Union in hopes of negotiating a new arrangement.
If no deal is agreed by March 20, "then it is highly likely the European Council at its meeting the following day would require a clear objective for any extension, not least to determine its length, and any extension beyond 30 June 2019 would require the United Kingdom to hold European Parliament elections in May 2019", Thursday's motion says.
The Elysee expressed "regret" for last night's vote, adding that "under no circumstances will we accept an extension without a credible alternative strategy on the UK's side."In a statement it said: "As the European Union has constantly and repeatedly said, the withdrawal agreement is not renegotiable".
Some hope a delay will result in either a second referendum or Brexit being scrapped alltogether, with others are aiming for a new deal.
MP for Houghton and Sunderland South, Bridget Phillipson, said: "I am not surprised that the Prime Minister's deal has yet again been overwhelmingly rejected by Parliament, given that it has not fundamentally changed since it was voted on in January". "This House will have to answer that question".
Europe's chief Brexit negotiator, Michel Barnier, sat down for an exclusive interview with Euronews' Daniel Cohn Bendit on Wednesday to discuss the possibility.
"Therefore, the House has to understand and accept that, if it is not willing to support a deal in the coming days, and as it is not willing to support leaving without a deal on 29 March, then it is suggesting that there will need to be a much longer extension to Article 50".
But Mrs May stressed that would not resolve the divisions in the Commons and could instead hand Brussels the power to set conditions on the kind of Brexit on offer "or even moving to a second referendum".
"The legal risk remains unchanged", he wrote Tuesday, noting there are "internationally lawful means" of leaving the backstop without European Union agreement.
Mr Lidington said: "Tonight we will be laying two new documents in the House; a joint legally-biding instrument on the Withdrawal Agreement and protocol on Northern Ireland and a joint statement to supplement the political declaration".
"Not for us, not for Britain and certainly not for our citizens", he said.