Asked on BBC Radio 4's Today programme whether she was prepared to delay a vote she is expected to lose, May said: "No".
She said MPs may have a role to play on deciding whether the United Kingdom would enter the backstop or extend a possible transition period - but she gave few details.
Before the prime minister appeared at the despatch box, her government had gone down to defeat for the third time in an hour.
The government had refused previous requests to publish the advice, which comes just a week before MPs vote on the deal itself, saying it would set a risky precedent if the Attorney General could not provide the Prime Minister with honest, confidential legal advice without fear of it being made public.
She told Today that she was staying in Government to make "absolutely sure" Britain does not end up in the backstop, saying: I am a very strong arch Brexiteer, I genuinely believe that we have a bright future ahead of us when we leave the EU.
But the source said the Prime Minisiter has fiercely opposed any such vote.
"First of all because in that backstop we will be making no financial obligation to the European Union; we will not be accepting free movement; and there will be very light-touch level-playing field requirements", she said.
"(It) would mean an immediate and probably indefinite loss of some security capability which, despite our best efforts, would likely cause some operational disruption when we leave", he said.
May hinted she might give parliament a greater role in deciding whether to start the backstop or extend a transition period under which more European Union membership terms would apply.
On Tuesday night, Mrs May had made a last-ditch attempt to rally MPs behind her Brexit deal after suffering the historic humiliation of seeing her Government found in contempt of Parliament.
Mr Benyon has consistently pledged his support to Mrs May throughout months of Brexit negotiations, having voiced his support for her previously failed Chequers Brexit plan and rejected amendments tabled by Jacob Rees-Mogg's European Research Group in June.
Prime Minister Theresa May leaving 10 Downing Street, London for the the House of Commons ahead of a five-day debate on her draft Brexit bill.
"The vote will take place on Tuesday as planned", May's spokeswoman said.
"This was not about doing deals, it was about listening", said one leading pro-Brexit lawmaker.