The Prime Minister warned that if the divorce deal is rejected again, the UK may "never leave".
MPs are due to vote on May's Brexit plan for a second time on Tuesday, two months after roundly rejecting it and less than three weeks before Britain's is due to leave the bloc.
So far there is little sign of May getting the concessions from Brussels that she says would reverse her previous defeat.
"It needs just one more push to address the final, specific concerns of our parliament," May said in a speech in Grimsby, a port town in northern England where 70 per cent of voters backed the decision to leave the EU in the 2016 referendum.
"So let's not hold back. Let's do what is necessary for MPs (members of parliament) to back the deal on Tuesday," she said, warning that "no-one knows what will happen" if it is rejected.
“We may not leave the EU for many months, we may leave without the protections the deal provides, we may never leave at all.”
She put pressure on her European counterparts, urging them to make concessions on the Irish border issue.
"The decisions the European Union makes over the next few days will have big impact on the outcome of the vote. It needs just one more final push to meet the specific concerns of our parliament," she said
London and Brussels are at loggerheads over the so-called Northern Irish backstop, which seeks to prevent the return of physical border controls between Northern Ireland and Ireland - the only land frontier between the United Kingdom and the bloc.
May wants legally binding assurances from the EU that Britain will not be trapped permanently in the backstop, which involves keeping Britain in a customs union with the bloc.
"The British People have already moved on. They're ready for this to be settled. So let's get it done," she said.
Many business leaders are alarmed at the prospect of leaving the bloc's single market, which underpins many of their operations, with no transition arrangements to soften the shock.
Irish Prime Minister Leo Varadkar said the British, not the EU, had to compromise, and the decision to leave the bloc had been "a problem of their own creation".
EU diplomats, responding to excerpts of May's speech released overnight, said she was preparing to blame the bloc for a fresh defeat of her plan.
"We are expecting a blame game after she loses the second 'meaningful vote' next week, so it looks like she is already preparing the ground for this," one of the diplomats said.
May has said that, if her plan is defeated on Tuesday, MPs will be able to vote on Wednesday and Thursday on whether they want to leave the bloc without a deal, or ask for a short delay to Brexit.
Her top lawyer returned empty-handed from negotiations with the EU this week, and the EU told Britain to rework its Irish backstop proposal by Friday.
EU Chief Brexit negotiator said “we are not interested in the blame game, we are interested in the result.”
