"My job as Prime Minister is to deliver for them, but also I've got to be hard-headed and practical about this and do it in a way that ensures we get the best interests for the United Kingdom".
She insisted the amendments did not deviate from her Brexit plan formally unveiled last week following months of cabinet infighting.
I think we're going to have a great trade deal.
She tweeted: "Govt are running scared and using silly tactics to avoid plotting by their own MPs".
Anna Soubry, a vocal proponent of keeping close ties with the European Union, told parliament: "One has to wonder now who's in charge in this country?"
On BBC Radio 4's Today programme he urged Tory colleagues who "want to get on with Brexit" to acknowledge that the Bill was "essential" and should not be impeded.
On two of Monday's votes her majority was cut to three, suggesting that May will struggle to get Brexit legislation through a polarised parliament, which could threaten any final approval of a Brexit agreement with the EU.
MPs are due to rise for the summer recess on July 24 but a motion tabled on Monday night would see the Commons rise on Thursday, with a vote pencilled in for Tuesday evening.
Opposition MP Angela Rayner branded the move "absolutely pathetic" and accused the government of being "afraid of their own MPs causing mischief".
Theresa May has appealed to warring Tory MPs to back her controversial blueprint for Brexit and avoid a disorderly withdrawal from the European Union which would damage Britain's interests. Her authority has been weakened with the resignations of major figures Boris Johnson and David Davis and a series of lesser officials who disagree with her Brexit plan.
May has been forced on the defensive following attacks on her strategy from all sides - including US President Donald Trump, who said during a visit to Britain last week it could kill a potential US-UK trade deal.
Former worldwide development secretary Priti Patel, who is proposing one of four amendments to the Taxation (Cross-border Trade) Bill, told BBC Radio 4's Westminster Hour the white paper had "many flaws around our independence and our ability to make free trade agreements".
A second mandates the country has a separate goods and services tax from Europe.
However, in a sign of just how volatile the party has become, former education secretary Justine Greening - who backed Remain - denounced the plan, saying it offered the "worst of both worlds" and called for a second referendum.
Her office has said there will be no second referendum under any conditions.
She said that would remove Britain's ability to have an independent trade policy and her government "will never stand for that".
"But rather than trying to fix the damage and negotiate with Brussels, the new Brexit Secretary has chose to take the evening off and attend a summer drinks reception".
"Brexit is enormously positive, a huge opportunity for the country".