Speaking to a packed meeting of Tory MPs - including Chancellor Philip Hammond, Brexit Secretary David Davis and Environment Secretary Michael Gove - May said: "We must think about the message Parliament will send to the European Union this week".
The battle now moves to the House of Lords, where the government will formally reveal how much it has conceded in the wording of a new amendment expected on Monday or Tuesday.
The Lib Dems, who identify strongly as an anti-Brexit party to the point of pushing for a second referendum and running by-elections in Remain-friendly seats on that platform, opposed the Government. "It enables parliament to dictate to the government their course of action in global negotiations".
The Lords passed an amendment stating that Brexit can not go ahead until a minister has presented a report setting out what the United Kingdom has done to try to negotiate continued customs union membership.
The Bracknell MP, who called for a second referendum on whatever deal Mrs May secures from the European Union, later told the Commons there was growing evidence that the Government's Brexit policy is "detrimental to the people we were elected to serve".
But May won a key vote in parliament on Tuesday with a compromise on plans to give lawmakers a "meaningful" vote later this year on the terms of Britain's exit from the EU.
The Bill will return to the Lords on June 18, kicking off a process of "parliamentary ping-pong" which sees it bounce from House to House until agreement is reached.
The government insisted it would not allow MPs to tie its hands in Brexit negotiations, despite being forced to offer a last-ditch concession to Tory rebels to stave off a House of Commons defeat.
The amendment would effectively give MPs the power to prevent the United Kingdom from opting to crash out of the European Union without a Brexit deal and is a major victory for Remain-supporting MPs in parliament.
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His statement follows a report from the New York Times, which criticized the White House for lacking a scientific advisory team. Between 1950 and 1953, during the Korean War, 35,000 American soldiers died and 7,700 are still listed as missing in action.
But if the amendments being debated in Parliament this week force a change to the government's negotiating strategy, the wound could yet reopen.
"Thirdly, we must under all circumstances respect the result of the referendum".
The Daily Express, another pro-Brexit tabloid, issued a thinly-veiled threat to lawmakers, saying they should "Ignore the will of the people at [their] peril".
Pro-Brexit tabloid the Sun warned lawmakers on Tuesday's front page that they had a choice: "Great Britain or great betrayal".
A file photograph of justice minister Phillip Lees.
In the tense atmosphere where it was not clear which way the vote would go, the government secured its victory only after offering concessions to one of the leaders of a group of Conservative lawmakers who were threatening to vote against May.
"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. After losing her party's majority in parliament at an ill-judged election past year, she now relies on the support of a small Northern Irish party and the distance between victory and defeat is narrow.
But once Britain leaves the E.U.it must find a way to regulate or otherwise account for goods crossing its border into Northern Ireland while keeping it open.
A paper laying out the U.K. government position, due to be published this month, has been delayed because the Cabinet can not agree on a united stance.