But the latest manoeuvre by a minority government that has been forced to compromise with parliament anxious some lawmakers who feared it would hand the European Union an incentive to withhold any agreement on an exit deal to force a softer Brexit.
Pro-EU lawmakers welcomed it as a signal that the government is giving up on a "no deal" Brexit.
The government won the vote after last-minute horse-trading, some of it in the open on the floor of the House of Commons - some behind closed doors.
Despite depending on the votes of the 10 DUP MPs for her precarious Commons majority, there were signs of cautious optimism among ministers that they would get the numbers to see off the revolt.
Asked what would happen if MPs rejected the deal, he said there would be no time to restart negotiations, with the United Kingdom leaving the European Union in March 2019.
Grieve had suggested in clause C of his alternative proposal that if there was still no deal by 15 February next year, the government would have had to hand over the reins to the House of Commons to set its Brexit strategy.
"But if the Lords amendments are allowed to stand, that negotiating position will be undermined".
Phillip Lee accused the government of trying to limit parliament's role in shaping Britain's departure from the European Union and said the government's Brexit strategy was detrimental to the British people.
The opposition leader said: "We can not settle for this".
"Thirdly, we must under all circumstances respect the result of the referendum".
Tory chief whip, Julian Smith, scurried up and down the green benches of the Commons, speaking urgently to groups of MPs including Grieve.
The solicitor general, Robert Buckland, said after the meeting: "We all hang together or we will hang separately".
She told BBC Radio 4's World At One that "at least half a dozen" junior ministers had been "very uncomfortable for some time" at the Government's direction on Brexit. Labour will only vote for a final Brexit deal if it delivers a strong relationship with the Single Market based on full tariff-free access and ensures no loss of rights and standards.
"It would be the end of the Conservative party if they succeed", he said. However, it is understood that she had concerns over the Lords amendment on the table.
If the government avoids defeat, is Brexit a done deal?
However, a compromise appeared in sight last night after Remainers and Brexiteers backed a call for ministers to report on attempts to agree a customs "arrangement".