Supporters of Hammond's new clause, which was backed by MPs from the main opposition Labor Party, were given hope of success when the government lost a vote on another aspect of its EU Trade Bill by just a handful of votes, 305 against 301 for the government.
The pressures building on the prime minister have come to a head in the last week, after the government finally published its strategy for leaving the European Union, which disappointed both sides of the divide.
One EU official said the extension could be given if member states see United Kingdom negotiators committed to hammering out a deal day and night.
May's plan has drawn criticism from members of her party as well as pro-Brexit members.
"The compromise plan that we have from Chequers doesn't achieve any of those".
By prevailing in Tuesday's vote, she avoided for now the prospect of having to go back on her word that Britain will not be part of any customs union after leaving the EU - something that would have enraged the pro-Brexit wing of her party.
Theresa May and Business Secretary, Greg Clark (right), arrive at the Farnborough International Airshow in Hampshire.
May's authority has been weakened with the resignations of major figures Boris Johnson and David Davis and a series of lesser officials who disagree with her Brexit plan.
Defeat on the amendment could have triggered a full-scale leadership crisis for the prime minister.
North Cornwall MP Scott Mann quit as a ministerial aide to the Treasury, the former postman saying he would not "deliver a watered down Brexit".
Ms Greening, the former education secretary, said the nation should be asked to decide between three options: Mrs May's plan for a softer Brexit, a hard "no deal" Brexit and staying in the European Union.
Brexiteers say this will keep Britain shackled powerless to the EU.
Prime Minister Theresa May won approval from the lower of house of parliament on Tuesday for a law needed to let Britain pursue an independent trade policy once it leaves the European Union. "There is not going to be a second referendum. under any circumstances", May's official spokesperson said. "Theresa May should finally accept that and get on with the job of negotiating for Britain".
Under the Article 50 withdrawal procedure, the United Kingdom has the right to ask for an extension of the talks, but the EU-27 unanimously need to agree to continue the negotiations.
Labour shadow chancellor John McDonnell said such a vote, listed for Tuesday evening, showed the government was in "chaos".
"But rather than trying to fix the damage and negotiate with Brussels, the new Brexit Secretary has chose to take the evening off and attend a summer drinks reception. This is simply not good enough".
Tuesday's legislation was technical in nature - focusing on converting trade deals between the European Union and third countries into bilateral deals with Britain - and was not originally meant to define new trade policy.
In a sign that he was keeping his powder dry, he said in an article for The Daily Telegraph that he would resist "for now" the temptation "to bang on about Brexit".
The Brazilian spiders are thought to have fled when a auto hit their containers which had been left in a vehicle park. We're also all going to be searching the area to make sure they're not here and then report it if they're here.
A British woman has been taken to hospital after being impaled in the leg by a parasol on a beach in the USA state of New Jersey. She was initially taken to Jersey Shore University Medical Centre on Monday but it is not known if she has since been discharged.
Reports today claimed Liverpool had made a £62m bid for the Brazil worldwide , with the goalkeeper agreeing terms with the Reds. If that's not definitive evidence that Alisson is DEFINITELY going to join Liverpool imminently, then I don't know what is.
It was later on the call that Schnatter said he used the actual word when pressed whether or not he was a racist. Schnatter opened up about his use of a racial slur in an interview with Louisville radio station WHAS on Friday.
The government narrowly won votes on the bill despite a rebellion by pro-EU Tories angry at the changes. And he said he was concerned the plan would become "even more compromised" in negotiations with the EU.
There is an exchange of gunfire - featuring the astonishing sight of a police officer firing 11 shots through his own windshield. Officers Umana and Soloman have been placed on routine paid administrative leave pending the outcome of the investigation.
Of course, take any and all alleged leaks with a grain of salt, but the Galaxy Note 9 will be revealed soon, for what it's worth. The front image shows the shattered screen of Galaxy Note 9 and the back has some minor scratches and dents.
US President Donald Trump has confirmed he is redesigning the presidential planes of Air Force One in red, white and blue. Trump tweeted that costs for the program were "out of control, more than $4 billion".
Last night, Trump revealed on Twitter that he was "looking forward to meeting with President Putin tomorrow". President Donald Trump had been aggressive in his demands to make members up their spending.
He has two years left on his contract with Chelsea , but he has indicated a desire to move on for a new challenge. German keeper Bernd Leno has been brought in by new Gunners boss Unai Emery this summer.
In Najaf, the protesters broke into Iraq's second-busiest airport, causing damages to the passenger terminal and delaying fights. Basra is Iraq's main producer of oil - the resource that accounts for at least 85 percent of the government's revenue.
Possible serial killer arrested in Houston after manhunt
On Saturday night, a young employee was shot to death inside the Mattress Firm at 7592 FM 1960, not far from Willowbrook Mall. Rodriguez also took off with Johnson's PT Cruiser, which he subsequently dumped in the parking lot of the Willowbrook Mall.
Robert Mueller asks judge to give immunity to five witnesses
Former Trump campaign manager Paul Manafort is shown in this booking photo in Alexanderia, Virginia, U.S., July 12, 2018. One trial is set for July 25 in Alexandria, Virginia, and the second case in Washington has a September 17 trial date.
No Man's Sky Trailer Reveals Upcoming Updates
Do you want to boldly go where no man has gone before? "The character customisation allows you to personalise your appearance". No Man's Sky will be launching on Xbox One alongside the NEXT update on 24th July in North America and 27th July in Europe.
Women at higher risk of mortality from heart failure
But previous studies have shown women are much more likely to die from heart attacks than men as they do not receive as good care. The researchers could not say why the death rates and hospital admissions for heart failure are so much higher for women.
'Baby Trump' balloon is coming to the U.S.
On Saturday morning, Jimenez tweeted , via @trumpbabytour, 'Thank you to all of your generous donations to make this happen. As of Monday night, the campaign has raised over $13,700 by 631 people over three days, far exceeding a goal of $4,500.
Batwoman Series In Development At The CW
Dries is writing the script and will executive produce the series alongside Sarah Schechter and Geoff Johns . But it's the first time an openly gay superhero would get top billing in a live-action show or movie.