The critical amendment adopted by the government on Monday said that HM Revenue & Customs could not collect duties or Value-Added Tax on goods on behalf of the European Union unless there was a reciprocal arrangement.
However, she has told unhappy lawmakers that they needed to back her or risk there being no Brexit at all.
Last week, members of the hard Brexit group put down four amendments to the taxation (cross-border trade) bill due to be debated on Monday evening, aimed at halting the customs plan announced by May at Chequers nine days ago.
Although the measures are unlikely to pass in the absence of Labour support, it could prove an opportunity for a show of strength by the rebels meant to pressurise her into retreat.
Supporters of the amendment, however, indicated it may not be moved to a vote on Monday night, partly because Remain-supporting Conservatives do not want to undermine the prime minister when she is vulnerable on her right flank.
He joins a number of Tory MPs in resigning their additional roles amid intense anger amongst Conservatives at Mrs May's approach, as agreed by ministers at an away day at her Chequers country retreat earlier this month.
The amendments relate to the customs section of the prime minister's Brexit plan, unveiled at a meeting of ministers at Chequers last week.
Mrs May has said she was forced to come forward with revised proposals after two options put forward by the European Union were deemed unacceptable.
"Our proposal sets out the right deal for the United Kingdom - honoring the democratic decision of the British people, protecting the integrity of our precious union, supporting growth, maintaining security and safeguarding British jobs", May said at the opening of the Farnborough Airshow.
"There is no way a government white paper can stipulate that 27 other countries are going to collect our tariffs for us".
A Labour source told HuffPost: "Theresa May sounds like she is running scared of her own MPs".
Former education secretary Justine Greening, who opposed Brexit, said May's plan to follow European Union rules on trade in goods without being able to influence them was "the worst of both worlds".
While heat from Remain wing of the party has also been turned up, Greening claimed the PM's Brexit plan, contrary to what the she claims, is not what people voted for.
Some in the pro-EU faction have also rejected the plan.
She said others were planning to try and bring down a bill that was essential to enable Britain to prepare for life outside the European Union, which would "risk our ability to make the necessary preparations for a no deal".
He told Today: "The amendments are to a Bill that is created to prepare for the world after Brexit, to be able to establish new customs regime that will be necessary".
Another pro-EU lawmaker Dominic Grieve, who has led previous efforts to get the government to soften its Brexit stance, said the party needed to accept compromises "or accept that Brexit can not be implemented and think again about what we are doing".