The Leave-supporting Conservative MP, who was elected after David Cameron stepped down following the Brexit vote, is the latest official to resign over Mrs May's proposals for the United Kingdom to leave the European Union.
Pro-EU Labour MP Chuka Umunna hit out at Labour Brexiteers who opposed the customs union amendment, saying: "It's very disappointing and our communities will question why Labour MPs are jeopardising jobs".
She told HuffPost UK: "Over my 29 years in Parliament, I have been censured many times by the CLP".
But despite the rebels' rejection of this overture, Mrs May emerged triumphant by a margin of just six votes, as the Commons rejected the key amendment by 307-301.
But while he told the News Letter that the DUP did not wish to "undermine" Mrs May's position, he said the party harboured "grave reservations" towards the Chequers plan.
Twelve Tory "remainer" MPs rebelled against the party whip and backed the amendment while four Labour Brexit-supporting MPs rebelled against their party whip and backed the government.
Twelve Conservative MPs rebelled against the government to vote for a proposal that would have kept the United Kingdom in the customs union if no alternative plan for frictionless trade with the EU had been agreed by January 2019.
During her visit this week, the prime minister is also due to speak to young people in Belfast about Northern Ireland's future.
One of the amendments practically says that the United Kingdom should not be collecting tariffs for Brussels unless the European Union does the same for Britain, one of the key ideas in May's original Brexit white paper that was created to keep the Irish border invisible.More news: Medical helicopter lands close to hospital near Thai cave
Mrs May went down to defeat on a separate amendment to her flagship Trade Bill, which will require her to seek continued United Kingdom participation in the EU's system for regulation of medicines after Brexit.
The entire trade bill passed by 31 votes and now moves to the House of Lords for further scrutiny before returning to the Commons for a final vote.
Britain's European Union membership was critical to United States interests, with the policy underpinning the agenda of all UK governments since Britain entered the European Union in 1975.
The commission said the Vote Leave group, backed by senior politicians who included former Foreign Secretary Boris Johnson, failed to declare 675,000 pounds ($1,304,476 NZD) it spent with Canadian data firm Aggregate IQ. The commission said Grimes and an official from Vote Leave have both been referred to police "in relation to false declarations of campaign spending".
The Prime Minister then heads for her most challenging date of the day, where she will appear before the 1922 Committee of backbench Tory MPs. He said we'd be responsible for a general election and putting Jeremy Corbyn in No 10.
He said Monday night's vote backing a commitment to no border in the Irish Sea, which is said to put the EU's "backstop" in jeopardy, should not give any cause for panic.
"The Government have a majority of 13 and there are 13 Scottish Tories".
"His speech will be a call for a change in policy, not a change of prime minister".