Debate will resume on Wednesday and the vote is officially slated for the week of January 14, but MPs look no closer to reaching agreement.
"The EU has made clear that this is the deal that is on the table", she said.
The Prime Minister also reaffirmed her opposition to a second referendum, claiming this would be "disrespecting" people who voted for Brexit.
Dame Caroline told BBC Radio 4's Westminster Hour: 'Crashing out of the European Union without a deal will cause job losses and bring to an end the renaissance of manufacturing that we've seen in regions like mine in the West Midlands, and both Jack Dromey and I know the human interest and impact of this'.
"If the deal is not voted on, this vote that is coming up, then actually we are going to be in uncharted territory", she told the BBC's Andrew Marr Show.
"What we are doing is highlighting the biggest poll on Brexit yet which shows that Labour will suffer its worst electoral defeat since the 1930s if it continues promising to enable some sort of Brexit to go ahead", he said.
"Don't let the search for the ideal become the enemy of the good, because the danger there is actually we end up with no Brexit at all", May said.
More than 200 MPs from different political parties have signed a letter to Theresa May, urging her to rule out a no-deal Brexit.
The UK's exit in March was "in danger" if MPs did not vote for it, she added. "If we have to have the vote 30 times, we will", they said.
It is unclear yet whether the amendment has enough support to pass.
"It's also impossible to say whether public opinion is in favour of a second referendum or not because answers to that question have varied basically as a function of the question that's being asked", he added.
In an interview with the BBC on Sunday, May pledged to set out new measures to address the contentious Northern Irish "backstop" clause in her withdrawal plans in a bid to win over sceptical legislators.
They range from a no-deal Brexit to not leaving at all.
Her views were echoed by her fellow shadow cabinet minister, Barry Gardiner, who said it would "make sense" to call another vote if Labour won power and secured a fresh deal with Brussels. But so far, Theresa May's inability to get her deal through parliament has alarmed business leaders and investors who fear the country is heading for a damaging no-deal Brexit.
The poll of more than 25,000 voters was commissioned by the People's Vote campaign, which is spearheading an increasingly vocal push for a second referendum on Brexit.
Meanwhile, one group of cross-party lawmakers is working on a plan to derail any prospect of a no-deal Brexit, which appears to be the most likely option if May's gambit fails.
May's Brexit deal is unpopular with British lawmakers across the spectrum, and the main sticking point is the insurance policy known as the "backstop" - a measure that would keep the United Kingdom tied to European Union customs rules in order to guarantee there is no hard border between the Republic of Ireland, an European Union member, and the U.K.'s Northern Ireland, which won't belong to the bloc after Brexit.