She needs to get a simple majority in House of Commons to get her Brexit deal approved.
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.
Many at Westminster believe that in that event MPs would vote to delay Britain's departure - to the fury of Brexiteers.
Cabinet ministers urged their Tory colleagues on Sunday to support May's deal, with Foreign Secretary Jeremy Hunt saying both the European Union and British parliamentarians need to be "realistic".
May had been tasked with securing changes to the so-called "backstop" protocol of the withdrawal agreement, which critics in the hardline wing of her ruling Conservative Party and the DUP say would trap the United Kingdom within the EU's trade rules indefinitely, or see Northern Ireland being treated differently from the rest of the country.
Birmingham vs. Villa marred by disgraceful scenes as fan punches Jack Grealish
Mitchell has been banned for life from Birmingham City Football Club where he had been a season ticket holder for 20 years. Gary Cooper appeared to be trying to join Arsenal players in celebrating a goal in the Premier League game on Sunday.
However Attorney General said that while it "reduced the risk" of the United Kingdom indefinitely remaining in the backstop, his legal opinion was unchanged that there was no unilateral way for the United Kingdom to exit the protocol.
Brexit-supporting lawmakers expressed suspicion at the haste of May's last-minute assurances and suggested a delay to allow sufficient analysis of them and Cox's advice.
British officials have said an exit agreement that locked Britain into a Customs Union with Europe was unacceptable but they struggled to secure changes in the deal agreed to late previous year.
Following that crushing defeat she agreed to renegotiate certain unpopular aspects of the agreement and hold another vote this Tuesday.
Talks will continue in Brussels but without a major breakthrough, May looks set to lose her second attempt to get lawmaker's approval and smooth Britain's exit from the European Union, its biggest shift in trade and foreign policy in more than 40 years. Hard-core Brexit supporters in May's Conservative Party and the prime minister's allies in Northern Ireland's Democratic Unionist Party both said they could not support the deal.
And he warned Tory MPs who plan to vote against the deal that it could mean Jeremy Corbyn becoming prime minister.
Jaguar that attacked selfie-taking woman won't be put down
A woman survived a close encounter with a jaguar after trying to take a selfie with it at an Arizona zoo on Saturday. The woman arm wounds caused excruciating pain, but all of her injuries were non-life-threatening.
Mr Lidington added the Attorney General would be publishing advice ahead of Tuesday's debate, but needed time to consider the new changes.
Lawmakers defeated May's deal by a whopping 230 votes in January, but May hoped the changes she secured from the bloc would be enough to persuade many to change their minds.
Politicians of every hue must overcome their differences and make avoiding a no-deal Brexit the absolute priority, starting with the vote in Parliament tomorrow.
In a letter outlining his thoughts over May's latest Brexit deal, Geoffrey Cox said the latest concessions from the EU don't eliminate the risk the country will remain entwined with the EU customs union indefinitely.
More than a third of Brits still want MPs to reject Theresa May's Brexit deal but opposition may be wavering, a new poll suggests - especially among Leave voters and Tories.
"I think that an important offer has again been made to Britain, and now it is, of course, for Britain to respond to these offers", she said in Berlin.
Kelly Released From Jail After Paying Child Support
The singer's defence attorney had previously said the singer was having financial difficulties and his finances were a "mess". That is all I can say right now", the 52-year-old singer said, before adding, "I love my fans", and dashing off.