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.
Whilst everyone gets very excited about Chequers tomorrow, truth is PM has been consistent with her #Brexit wishlist from day one - control of money, borders and laws. We should support her, get behind her and deliver precisely those things!— Ben Bradley MP (@bbradleymp) July 5, 2018
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.
And Henry Smith, the MP for Crawley, disclosed that he had turned down an invitation from Downing Street to watch England's World Cup semi-final on Wednesday, tweeting:
Received this invite to watch tomorrow’s England-Croatia World Cup semi-final in 10 Downing Street. Seeing as the Prime Minister isn’t bringing Brexit home I’m concerned attending would be a bad omen for football coming home...I’ll pass. pic.twitter.com/1BjH6uczZG— Henry Smith MP (@HenrySmithUK) July 10, 2018
Trump: There's a lot going on
Ahead of his first visit to the country as US President, Donald Trump said the UK was "somewhat in turmoil" and "it is up to the people" whether Theresa May stays as prime minister.
Mr Trump, who arrives in the UK on Thursday after attending the Nato summit in Brussels, told reporters before leaving Washington there were "a lot of things going on" in the UK at the moment.
He said he got on well with Mrs May and had "always liked" Boris Johnson, who quit as foreign secretary on Monday, describing him as a "friend of mine".
Mr Trump, who has called on other Nato members to pay more for their own defence, joked that his meeting with Russian leader Vladimir Putin in Helsinki on Monday "may be the easiest of all".
Merkel: There's progress
The prime minister has chaired the first meeting of her new-look cabinet, after the departures of Mr Johnson and former Brexit Secretary David Davis
The new Foreign Secretary Jeremy Hunt urged all ministers to stand behind Mrs May in pursuit of an agreement with the EU based on the approach agreed at Chequers.
Irish Prime Minister Leo Varadkar, who has insisted any Brexit deal must guarantee there is no "hard border" on the island of Ireland, has suggested the Chequers agreement might represent a breakthrough.
"If the UK is able to relax some of its red lines, then the European Union should be flexible too," he told the Irish Parliament. "I think perhaps we are now entering into that space."
German Chancellor Angela Merkel, speaking at a summit for the Western Balkans in London, said it was good that the UK had put proposals on the table and the EU would issue a "common response" in due course.
"We have made progress," she told reporters.
And the EU's negotiator Michel Barnier said 80% of the detail of the UK's withdrawal had been settled and he was now prepared to start talking about a "very ambitious" trade agreement with the UK.