An aide to Defense Secretary Gavin Williamson has quit in protest at the Prime Minister's Brexit deal.
Colchester MP Will Quince hit out on the backstop plan to avoid a hard border with Ireland, saying it could have been in the UK to anything in desperation "to get out of the situation.
Writing in the Sunday Telegraph, Mr Quince said: "I do not want to explain my constituents why.
"Unless and until this is amended, the Withdrawal Agreement can not receive my support."
Theresa May faces widespread opposition to her plan across the Commons, including both Remain and Leave-supporting wings of her own party, ahead of the December 11 vote.
So on Saturday, Work and Pensions Secretary Amber Rudd voiced support for a Norway-style model as to alternative to the Prime Ministers Brexit deal if the Withdrawal Agreement is thrown out by MPs.
Rudd is the first Cabinet minister to discuss the merits of a "Plan B".
And in a further apparent departure from No 10's official stance, Ms Rudd would not rule out a second referendum and suggested they would remain in the EU if one was held.
The Cabinet Minister Sir Hugo Swire in an attempt to win over wavering Eurosceptics.
The alteration would mean Parliament would have to endure the backstop arrangement, put a one-year limit on it and seek assurances from the EU that the backstop would be temporary.