Walker, who is also chairman of the Commons procedure committee, said if MPs reject her deal the prime minister could call an election at the end of this week to take place in seven weeks time.
391 MPs voted against it while 242 voted for it - a majority of 149.
"Quite clearly, no-deal must be taken off the table", he added.
"A WTO or "No deal" Brexit would be costly for businesses and consumers and would fly in the face of the promises I made before I was re-elected in 2017".
Prime Minister Theresa May has given up any pretence of leading Britain by allowing her lawmakers to vote according to their own beliefs rather than along party lines on Wednesday, the opposition Labour Party said on Tuesday.
Those Tory Brexiter MPs who WANT to believe the EU has no desire to trap the United Kingdom in the customs union via the Northern Ireland backstop will be reassured by the agreement between Theresa May and Jean-Claude Juncker on a new legal instrument saying the EU must negotiate in good faith to avoid the backstop coming into force at all or for long.
Labour Party leader Jeremy Corbyn said the government must accept its deal does not have the support of the House.
Labour MPs indicated they meant to vote against a no-deal Brexit on Wednesday.
Amid speculation about how long she can survive in Downing Street, the Prime Minister's aides insisted she had not considered resigning.
"And people in the Borders are exhausted of the constant debate about Brexit and just want our country to move on". More time will not significantly change the options on the table-Conservative MPs may want to note too that their voters are shifting in favour of the deal, with 54 per cent now backing it.
Asked if the deal was sunk, Welsh Secretary Alun Cairns said: "I wouldn't write the deal off just yet, I think there's many more twists and turns to come".
The move - branded the "Malthouse Plan B Amendment" - would see Article 50 extended until May 22.
Pro-EU Labour Cardiff Central MP Jo Stevens said: "You've got to wonder what more [Theresa May] could try and do".
Speaking in Strasbourg, where the European Parliament is gathering for a debate on Brexit ahead of the next European Council summit, the EU's chief negotiator Michel Barnier said: 'Again the House of Commons says what it doesn't want.
She added: "I don't believe there is a deal out there that is better than we have now".