The YouGov survey shows the exit deal enjoys the support of only 38 percent of members of her own party.
Also, 76 percent of those polled said warnings over a no-deal split are exaggerated or invented, Presstv Reported.
May believed opposition to her deal might soften after the Christmas holiday, but the new poll found that Conservative Party grassroots would overwhelmingly prefer to leave the EU without a deal than stick with the agreement negotiated by the Tory premier.
The UK parliament will vote on the prime minister’s deal in the third week of this month.
Without a parliamentary approval, the UK will either have to crash out of the EU without a deal or delay Brexit.
May’s deal has been widely criticized by both allies and rivals.
The British leader has warned that rejection of her plan would risk a chaotic exit from the EU or not leaving at all.
However she has failed to persuade many skeptical MPs to back her deal, especially as EU leaders have indicated that the agreement is "not open for renegotiation."
Meanwhile, UK Labour Party leader Jeremy Corbyn is facing further pressure to back a second Brexit referendum after polling showed clear support among party members for another vote.
A study of more than 1,000 members found 72 percent want Corbyn to throw his weight behind a so-called People's Vote, a pro-EU campaign group calling for a public vote on the final Brexit deal.
Among those urging Britons to vote in a second referendum is former Prime Minister Tony Blair — a high-profile figure.
In December, Blair said May’s deal had pleased neither “Brexiteers” nor “Remainers,” adding that a second Brexit referendum should be a choice between remaining and a hard Brexit.
The British prime minister has time and again ruled out a second referendum as an option.