May's majority was cut to just three votes after she adopted Brexiteer amendments to a key piece of customs legislation, and the proposals narrowly passed through the House of Commons late on Monday.
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.
Remainer conservative MPs warned that the Brexit plan amended by hardliners increase the likelihood of a no-deal divorce, and that prospect is becoming more tangible in Brussels as well.
Some MPs have tabled an amendment to the Taxation (Cross-border Trade) Bill, also known as the customs bill, seeking a new customs union with the EU, which May has strongly rejected.
And the gloomy forecast of the furious Government minister I bumped into as he arrived to vote on the trade bill - that this Tory split will bring down the Government - will probably be proved to have been accurate as well.
Liberal Democrat Brexit spokesman Tom Brake said: "Today we have seen the truly calamitous state of the Tory party, as once again the Prime Minister is forced to concede ground to hold together her unholy alliance of MPs".
But the climbdown, a hasty decision mid-afternoon - which smacked of panic - to accept four amendments to the Bill from Mr Rees-Mogg's European Research Group, nearly backfired spectacularly.
Amazon suffers glitch as Prime Day kicks off
Based on its data, Prime Day was the biggest online shopping day in the third quarter across several categories. ET Monday launch in the USA got only images of dogs - some quite abashed-looking - with the words, "Uh-oh".
"We were all set [on the Remain side] to drop all our amendments and back it, then suddenly we had these rather extreme last minute manoeuvres, which seem to us to deviate the prime minister from her plan and we weren't prepared to do that".
"She can not be held hostage by them every time there is a hard vote in the House of Commons - and it now looks as though the Chequers plan is completely falling apart", Ms Blackman said.
Meanwhile Boris Johnson, in his first public intervention since his resignation last week, appealed for people to take a more positive view of Britain's prospects outside the EU. "And whether she can continue", Tory lawmaker George Freeman, who used to head May's policy board, said in a posting on Instagram.
She insisted it would allow Britain to control migration, end the jurisdiction of European Union courts and forge its own trade policy - despite US President Donald Trump saying it could "kill" a US-UK trade deal.
"The Tory government is riding roughshod over the Scottish Parliament's voice on Brexit".
She told BBC Radio 4's Today programme: "What was agreed at Chequers wasn't flawless to us, wasn't ideal to Leavers either, but I think the prime minister had worked exceptionally hard to find a decent first pitch to put to the European Union and move forward from that". I think it was a genuine clever attempt at a compromise that could work. Further tests will come as the Trade Bill is debated on Tuesday.
He said: "I can't possibly dress it up in any other words than it's an absolute shambles and a self-inflicted shambles by Number 10".
Amazon said on Twitter that "some customers are having difficulty shopping, and we're working to resolve this issue quickly,". The Ver.di services union said workers at six German sites went on strike Tuesday to protest a lack of health benefits.
Authorities say they don't plan to charge the driver who accidentally hit DeSandra but charges against her father are pending. Thomas thought her father was dead, got out of the vehicle with her backpack and climbed over a fence. "She was so helpful".
Trump said he and Putin would discuss a range of issues, from trade to the military, along with missiles and China. A one-on-one meeting between the two men went on for more than two hours rather than the scheduled 90 minutes.
The starlet sports kohl smudged eyes and an intense look as she is seen surrounded by people. "Hope you all also give it love". Talking about her birthday plans, Katrina Kaif said that she wants to spend the special time with her loved ones.
However, Gary Sanchez hit seven more home runs while playing eight more games in the second half compared to the first. Judge, the Yankees slugger and defending home run derby champion, said "I want to stay healthy" in turning down a spot.
Reportedly she was in the hospital for the last 10 days. "Infact we were planning to visit Rita's house for a small get-together". Zarina Wahab , who was her FTII batch mate, told India Times website, "Rita Bhaduri was the prettiest lady in our batch".
The prank comes after Sarah Palin accused Cohen, 46, of duping her into doing an interview by posing as a wounded veteran. Though Ruddick uses a mobility scooter, he explains that it's just "to conserve my body's finite energy".
Trump sees progress on an arms control treaty as the likeliest area of progress for the Trump-Putin summit, the source said. But Trump has vowed that he can handle Putin, whom he has taken to referring to as a "competitor" rather than an adversary.
The drugs might contain the ingredient valsartan, which is used to treat high blood pressure and heart failure , the FDA said. The drug contains NDMA, which has been classified as a "probable human carcinogen", which means it could cause cancer.
Theresa May braced for showdown with Brexit rebels
It is with a great deal of sadness that I have tendered my resignation as a Parliamentary Private Secretary at the Treasury. On Monday, Brexit supporters targeted the government's so-called customs bill, hoping to toughen up her plans.
Usain Bolt in shock A-League move
FFA has a pot of $3 million, provided by Fox Sports, to spend on marquee players for the upcoming season. The A-League is the country's top professional soccer tier and run by Football Federation Australia .
Heat warning for Kelowna and Penticton
The Fraser Valley community of Lytton claimed the title of Canadian hot spot on Sunday at 37.1 C and is forecast to reach 39 C. The City of Toronto also issued its own warning over the weekend following prolonged heat and humidity.
Bryce Harper wins 2018 Home Run Derby
Freeman was the oldest player in the field at 28, and the first Braves participant since Andruw Jones in 2005. The Phillies first baseman, who is the eighth seed, stunned top-seeded Jesus Aguilar in the first round.