The government averted a rebellion on Tuesday over whether Parliament should have a decisive say in such a scenario.
MPs said they were offered, in a last-minute concession, real "input" if no deal with the European Union was done by December.
Ministers had initially refused to even consider Grieve's amendment but moved to accept it at least in part, after whips signaled that the government were likely to lose in the Commons.
Exactly a year ago, it looked like May did not have long left in office.
"I've been through this before when in opposition and now that when we're in Government, because if the House makes the concession of allowing the dialogue to continue and I can see the merit of that happening, it has got to be done in good faith".
They are rallying around an amendment giving the House of Commons power to send the government back to the negotiating table with Brussels if lawmakers don't like the terms of the Brexit deal struck with the EU.
This led him not to force his own amendment to a vote, while the potential rebels backed away from voting against the government on a similar House of Lords amendment, thereby allowing ministers to remove the peers' changes to the bill.
During her speech former Tory minister Anna Soubry hit out at the "deeply-divided cabinet", telling MPs: "Never before have we been in a situation where we have a cabinet who is so divided".
In such an event, he said Parliament should be able to flex its muscles by requiring ministers to come forward with a plan of action, which MPs would be able to debate and vote on.
Hours before the debate began, a justice minister resigned in protest at what he called its "wish to limit" the role of parliament in shaping Brexit.
"I absolutely trust what the Prime Minister says to us", he told BBC Radio 4's PM programme.
"If it were to turn out there was a problem, we will deal with it".
Theresa May saw off a revolt from the pro-European wing of her fractured party, averting what could have been a major political crisis.
"What it does is put in place a structure if things do go as planned", she said. "There could be a confidence motion [in the prime minister] or an early general election".
Which side won on Tuesday will become much clearer in the next few days, when the government amendment is tabled in black and white. The government fears a weakened negotiating position.
"Time will tell as to whether this is just another attempt to buy off the rebels or a real attempt at consensus. There is an expectation that a discussion will yield fruit and I am not saying it won't".
"The people want us to leave the EU".
Lawmakers kicked off two days of debate on Tuesday on changes to May's Brexit blueprint, or European Union withdrawal bill, after the upper house of parliament, the House of Lords, introduced 15 changes.
To buy off a group of Tory rebels - whose ranks were boosted by the shock resignation of Justice Minister Phillip Lee Tuesday morning - the prime minister agreed in principle, according to the rebels, to write into law a new deadline in the Brexit talks: November 30, 2018.
In an earlier vote, MPs voted by 328 votes to 297 to disagree with another Lords amendment which was linked to changes to the day Britain leaves the EU.