Only 19 per cent of voters believe the surprise agreement struck with Brussels last week is a good deal and only 3 per cent described it as “very good”.
The proportion not knowing enough about it to offer an opinion has fallen from 45 per cent to 34 per cent – with most who have made up their minds refusing to give their endorsement.
Furthermore, the survey suggested the prime minister has failed in his strategy of pinning the blame on Labour for the failure to deliver on his “do or die” pledge to leave the EU by 31 October.
Over half the public blamed “MPs on all sides” suggesting the Tories will struggle to make the controversy a vote-winner in a general election.
Nevertheless, the poll, by YouGov for The Times, shows the Conservatives are maintaining their huge overall lead, holding out the promise of a Commons majority if the election is held.
The election would also be dominated by Brexit, it seems, with 59 per cent citing leaving the EU as a priority in deciding how to vote, followed by health on 37 per cent and the economy on 29 per cent.
However, it appears unlikely to go ahead on 12 December, as Mr Johnson demanded, with opposition parties set to block a trigger motion on Monday.
A two-thirds majority is needed in the Commons to overturn the Fixed-term Parliaments Act, which stipulates no election before May 2022 – meaning Labour has an effective veto.
The poll found that 28 per cent of voters consider the deal to be bad, up five points from last week, while 20 per cent thought it was neither good nor bad, up from 15 per cent when the agreement was struck.
Only 23 per cent cited leaving the EU on Mr Johnson’s terms as their preferred Brexit outcome, against 20 per cent wanting no deal and 37 per cent backing Remain.
But only 29 per cent said parliament should reject the deal, while 40 per cent thought MPs should vote to implement it.
YouGov questioned 1,634 voters between 24 and 25 October