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.
Conservative former minister Anna Soubry said the abuse of MPs who speak out against the government's Brexit policy "simply has to stop".
"First, we must never do anything that undermines the Government's negotiating position or encourages delays in the negotiations", Mr Davis said.
"I am very pleased that the government has listened to the concerns of many colleagues and has responded positively to the need to amend the bill further to provide a proper mechanism to enable Parliament to act, where necessary, if there is no deal or a deal is rejected by negotiations", Grieve said.
Either way, the chances are increasing that Parliament will get a greater say over Brexit.
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.
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.
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.
Sepp Blatter to attend World Cup as personal guest of Vladimir Putin
Either North America or Morocco will earn the right to host the 2026 World Cup when the vote is conducted at the FIFA Congress in Moscow.
Labour MPs are expected to rebel against their party whip in significant numbers to vote in favour of a Lords amendment to keep the United Kingdom in a Norway-style trading arrangement post-Brexit.
"I expect the government to honour its commitments and I expect the PM to honour her commitments and I have no reason to distrust the approach she took with us", Mr Grieve told the BBC's Newsnight.
No - Even with the support of 10 Democratic Unionist Party MPs, May has a working majority of just 13 in the Commons, which means she can be defeated by a rebellion of as few as seven Tory backbenchers.
"It completely undermines the Government's negotiating position with the European Union". "At the start of this process, we had no vote in Parliament on the final deal at all".
"The decision was taken by the people, we gave them that decision and we have to stand by it", said Conservative MP Bill Cash. "There could be a confidence motion [in the prime minister] or an early general election". May's been resisting the demand because she doesn't want her hands to be tied during the talks.
During a five-hour debate, MPs reinstated the precise day the United Kingdom will leave the European Union - 29 March 2019 - in the proposed legislation while backing an amendment on the Irish border, guaranteeing there will be no new border arrangements without the agreement of the United Kingdom and Irish authorities.
Dismissing the Government's compromise, she tweeted: "Merely issuing a statement in response would make it a meaningless final vote".
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.