'If a bad Brexit is forced upon our country and jobs and the economy are not protected, many of our people who have suffered from eight years of austerity will suffer even more, ' he said.
She said the agreement she negotiated with the European Union was "a good deal and one that delivers on the referendum".
Sky News understands Mrs May would struggle to delay the vote because the debate leading up to it has already started - meaning she would need to win another vote adding an amendment to push it back.
But EU negotiator Michel Barnier said on Thursday the deal was the best Britain will get, while British finance minister Philip Hammond said it was "simply a delusion" to think the agreement could be renegotiated if parliament rejects it.
Supporters of a clean break with the European Union say the backstop, meant to ensure no hard border between British-ruled Northern Ireland and EU-member Ireland, could leave Britain forced to accept European Union regulations indefinitely, or Northern Ireland treated differently from the rest of the United Kingdom.
May signalled that she was determined to plough on with a vote and suggested a "parliamentary lock" on the Irish backstop could persuade more MPs to back it.
"People have a concern of the backstop, that we could be in it indefinitely".
The Times reported [£] that some cabinet members, including the defence secretary, Gavin Williamson, were pushing for a delay to the vote over fears the defeat would be so large it could bring down the government.
Revista: Pantone anunció cuál será el color del 2019
El proceso de selección de Color del año requiere una consideración cuidadosa y un análisis de tendencias . Así, Living Coral evocará la forma de los arrecifes y a un ecosistema naturalmente vivo y cromático .
It is a key condition of the continued support of the Northern Irish Democratic Unionist Party, which is propping up May's minority government.
The advice, which is only six pages long, is being avidly read by MPs in the House of Commons in real time, suggests that because of the nature of the Irish backstop arrangement in the Brexit deal, the United Kingdom could be trapped in "protracted and repeated rounds of negotiations" for years ahead.
"In a sign of the ever-growing divisions over Brexit, the BBC announced that it has abandoned plans for a proposed televised debate between May and Opposition leader Jeremy Corbyn on Sunday after both sides failed to agree on a format".
When asked repeatedly what her "Plan B" would be if her deal was rejected, she did not directly answer the questions.
"There are questions about how decisions are taken as to whether we go into the backstop, because that isn't an automatic", she said.
"There will be a choice between going into the backstop and extending the transition period, ' she told the BBC's Today Programme".
"All week we have heard from Government ministers that releasing this information could harm the national interest".
It then opens up the field to a no-deal chaotic Brexit without any exit arrangements in place, a scenario which also has few takers in the UK Parliament and is expected to further dent May's already tenuous hold on leadership.