It is an “absolute priority” for the government to leave the EU by 23 May to avoid having to take part in European elections, Jeremy Hunt has said.
The foreign secretary said the public would find it “hugely disappointing” to be asked to send MEPs to Brussels.
Asked if it could be a disaster for the Tories, he told the BBC “in terms of polling it certainly looks that way”.
Some local Tory activists have signalled they will not campaign and regard the polls as a “distraction”.
Last week, the EU agreed a new Brexit deadline of 31 October.
Talks between the government and Labour are set to continue over the Easter parliamentary recess in the hope of finding an agreement that will be acceptable to MPs.