The prime minister revealed advice in an interview with the BBC overnight, as Mr Trump left Scotland for his talks with Russian President Vladimir Putin in Finland.
Former global development secretary Priti Patel, who is proposing one of four amendments to the Taxation (Cross-border Trade) Bill, told BBC Radio 4's Westminster Hour the white paper had "many flaws around our independence and our ability to make free trade agreements".
And he's angry the PM went over his head with the Brexit white paper.
And when pressed in a newspaper interview afterwards, Mr Trump still declined to reveal what his suggestion was.
Trump has often begun calls by asking her to rush the process.
She acknowledged that some lawmakers had doubts about her plans to stick to a "common rule book" with the bloc for goods and agricultural products in return for free trade, without tariffs or border customs checks, but insisted she couldn't see a viable alternative.
Party chiefs spent Sunday trying to assess the extent of discontent with her Brexit stance as they set their sights on reaching next week's parliamentary recess without further damage to her leadership.
"And this could lead to a damaging and disorderly Brexit because without this bill passing we would not be able to retain the benefits of more than 40 existing trade arrangements; and neither will we have the means to protect consumers, industries and workers from being undercut by unfairly traded goods in a post-Brexit Britain".
He added: "I can fully understand why should thought it was a bit tough and maybe someday she'll do that".
"And it can not be the destruction of integrated supply chains and just-in-time processes on which jobs and livelihoods depend".
She said it would allow the United Kingdom to strike trade deals with other nations, end free movement of people, and end the jurisdiction of the European Court of Justice.
"It would have been more straightforward to admit that no real Brexit was the intention all along rather than trying to gull Brexiteers".
However, in a sign of just how volatile the party has become, former education secretary Justine Greening - who backed Remain - denounced the plan, saying it offered the "worst of both worlds" and called for a second referendum.
The warning came after key cabinet members David Davis, the Brexit secretary, and foreign secretary Boris Johnson quit over the proposed deal she presented during an away day at her country house, Chequers, last Friday.
"It does appear to me that there has been a year's worth of cloak and dagger to land us into the Chequers position", he told The Sunday Telegraph. 'An establishment elite who never accepted the fundamental right of the public to choose democratically their institutions, are working towards overturning them'.