It would also give hard Brexiteers the chance to "scupper a good deal", she claimed.
The House of Commons voted by a wide margin against a call to join the European Economic Area - a club that includes the EU nations and Norway - after Conservative and opposition Labour leaderships opposed it.
May had faced the prospect of losing the vote on the customs union after rebels had indicated their support for a change introduced by the House of Lords to require ministers to report what efforts they had made to secure a customs union.
But it is likely only a temporary reprieve.
- How about the customs union? The withdrawal bill promises that the border will stay open and there will be no "physical infrastructure, including border posts, or checks and controls". "So we are partway through discussions and there is more to come", she said.
Theresa May has found herself in a fresh standoff with Conservative rebels after Downing Street signalled it has no intention of discussing a central aspect of their demands.
Writing in The Guardian, shadow Brexit secretary Sir Keir Starmer said: "Instead of negotiating for Britain, the Prime Minister is lurching from crisis to crisis, increasing the risk that the talks break down, and we crash out without an agreement".
She said: "I can not countenance Parliament being able to overturn the will of the British people: Parliament gave the decision to the British people, the British people voted to leave the European Union and as Prime Minister I'm determined to deliver that".
Labour shadow minister Laura Smith and four other opposition MPs have resigned from party roles, over a whip forbidding them from voting in favour of the Lords amendment to keep the United Kingdom in the European Economic Area (EEA).
"I think that the British political system doesn't really have the will to implement Brexit, never wanted to do it and it isn't intending to do it now".
New Zealand Prime Minister welcomes newborn girl ‘to our village’
The 37-year-old will take six weeks of maternity leave , and has now passed on her duties to Deputy Prime Minister Winston Peters. He said Ardern should be allowed to acclimatise to motherhood and not be held to higher standards because she was prime minister.
Tory backbencher Simon Clarke told MailOnline: 'MPs gave the British people the right to make this decision and they voted to leave the European Union - including Philip Lee's own constituents in Bracknell by some 53 per cent.
On Wednesday, parliament will consider a challenge to her commitment to leave the EU's single market and customs union, which will transform Britain's future trading relationships for many years to come.
The House of Commons was holding a second day of votes on the European Union Withdrawal Bill, meant to disentangle Britain from the bloc.
Two days of debate on the laws that will end Britain's European Union membership have crystallised long-running divisions within May's party about the best strategy for leaving the European Union, bringing to a head issues that will determine the relationship between the world's fifth-largest economy and its biggest trading bloc.
May, who leads a minority government propped up by the small Northern Irish Democratic Unionist Party (DUP), conceded that "we need parliamentary support" to implement Brexit.
A paper laying out the U.K. government position, due to be published this month, has been delayed because the Cabinet can not agree on a united stance. Scottish National Party lawmakers walked out of the House of Commons Wednesday to protest the short amount of time given to debate Scotland-related issues the day before - 20 minutes out of a six-hour session.
The disagreement centers on whether the government agreed to consider a specific clause of the rebel proposal that would hand parliament control of the Brexit process if ministers are unable to strike an exit deal by February 15, 2019.
Earlier, tensions over the bill's provisions on devolution boiled over when SNP MPs walked out of the Commons after their leader Ian Blackford was ejected.
"Scotland's voice has not been heard", said Blackford, who was expelled from the chamber for repeatedly challenging the Speaker on the issue, sparking a walkout by his colleagues.