Two vice-chairs of the Conservative Party are quitting their posts in protest at Theresa May’s Chequers Brexit compromise plan.
Maria Caulfield and Ben Bradley warned the PM her plan would not capitalise on the opportunities of Brexit.
“This policy will be bad for our country and bad for the party,” Ms Caulfield said.
Foreign Secretary Boris Johnson and Brexit Secretary David Davis have already quit over the proposals.
Ahead of his first visit to the country as US President on Thursday, Donald Trump said the UK was “somewhat in turmoil” and it was “up to the people” whether Theresa May stays as prime minister.
He also praised Mr Johnson, describing him as a “good friend of mine”.
Mrs May says the proposed new relationship with the EU will “honour the result of the referendum” and allow the UK to “take back control of our borders, our law and our money”.
Speaking at a press conference alongside German Chancellor Angela Merkel, the prime minister said her plan would allow for a “smooth and orderly Brexit”, protecting jobs and livelihoods.
It would see the UK agreeing a “common rulebook” with the EU for trading in goods, in an attempt to minimise friction for trade at borders.
But some Tories are unhappy, saying it will leave the UK tied closely to EU rules and prevent it from striking its own trade deals in years to come. More details are expected on Thursday in a White Paper.
Ms Caulfield, who was vice chairwoman for women, supported Leave in the EU referendum. Mr Bradley – who backed Remain – had a brief trying to appeal to young voters.
The Conservatives have nine vice chairmen in total, appointed in January’s reshuffle.
In her resignation letter to Mrs May, Ms Caulfield – the MP for Lewes in Sussex – said the proposed new trading relationship with the EU did not “fully embrace the opportunities that Brexit can provide”.
Mr Bradley, who posted a positive message of support for Mrs May before Friday’s Chequers meeting, said he could not now “with any sincerity defend this course” to voters in his Leave-backing constituency of Mansfield.
He criticised the decision to adopt a “backstop” position on customs to avoid a hard border in Northern Ireland, saying it was becoming “the barrier to the kind of wide-ranging free trade agreement with the EU that many in our party and the country would like to see”.
Amid continuing unrest on the Tory benches, Andrew Bridgen became the first Conservative MP to publicly confirm he had sent a letter calling for a vote of confidence in Mrs May.
Under Conservative Party rules, it requires 15% of all Tory MPs – currently 48 – to write to the chairman of the backbench 1922 Committee to trigger a vote of confidence in the leader.