The survey showed 45 percent now wanted to leave the EU, ahead of 36 percent who wanted Britain to remain in the 28-member club.
That marked a three point rise for those in favour of a so-called “Brexit” since a poll taken a week earlier, before the proposals were published.
Cameron has been seeking to renegotiate Britain’s relationship with the EU before a public referendum on whether to remain a member, which could be held as early as June.
The proposed changes include a four-year “emergency brake” limiting welfare payments to migrants, as well as a “red card” system for national parliaments to overrule draft EU laws.
The poll of 1,675 adults in Britain was conduced by survey company YouGov on February 3-4 for The Times newspaper.
It showed support for staying in the bloc had dropped by two points, while 19 percent said they did not know or would not vote.
Pollster YouGov noted that the survey had been taken amid “negative headlines” about the proposed deal, which was criticised as a “joke” and a “delusion” by newspaper front pages.
“All of the changes proposed within the deal are popular… However only 22 percent say it’s a good deal, and 56 percent say the changes do not go far enough,” wrote YouGov UK online editor Will Dahlgreen on the results.
It is the first poll to be taken since the announcement of the proposals, and comes after sources close to negotiations in Brussels told AFP that no European leaders were satisfied with the draft deal.
Cameron is set for two weeks of whirlwind diplomacy to try to win over other EU leaders to agree a deal by a summit on February 18-19.