"Actually, no, we're going into negotiations with them", she said.
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".
Trump said in an interview published in Rupert Murdoch's Sun newspaper on Friday that May had not taken his advice on Brexit, which was just one of many comments made by the president about her exit plans.
"Don't walk away from those negotiations because then you'll be stuck".
Referring to May's Brexit proposals, Trump told the Sun, Britain's top-selling newspaper, "If they do a deal like that, we would be dealing with the European Union instead of dealing with the United Kingdom, so it will probably kill the deal".
But hours later he said a US-UK trade deal would "absolutely be possible".
Leading Brexiteers continue to criticize her openly, with Jacob Rees-Mogg telling the BBC that May is a "Remainer" and her White Paper is a "bad deal for Britain".
Amid rising backbench anger, MPs are set to vote on Monday on a series of Commons amendments meant to wreck her Chequers plan for a "common rule book" covering a new "UK-EU free trade area". He told journalists he had given the PM advice about how to handle Brexit, but Mrs May had thought it "too brutal".
Donald Trump opens up about his conversation with the Queen
While there was a seriousness to their protests, numerous signs have gone viral for their sarcastic and hilarious nature. Trump did say he admires the queen and found her to be "incredible", "sharp" and "beautiful".
Greening said that with divisions in the Conservatives and the opposition Labour Party over how to proceed with Brexit, there should be another vote, with the public able to choose between May's plans, a "no-deal" break with the European Union or remaining in the bloc. Scott Mann, MP for North Cornwall, who was a PPS to the Treasury team, says he was not prepared to accept a "watered down Brexit". She said she and other senior Tory lawmakers favor a new vote.
May has been forced on the defensive following attacks on her strategy from all sides - including US President Donald Trump, who said during a visit to Britain last week it could kill a potential US-UK trade deal.
"My message to the country this weekend is simple: we need to keep our eyes on the prize", May wrote on Facebook. 'If we don't, we risk ending up with no Brexit at all'.
With less than nine months to go before the country is due to leave the European Union next March, the political elite and business leaders remain deeply divided over what form Brexit should take.
Putin summit: U.S. president under fire over poll meddling comments
Trump then said, for the first time , that he believes Putin: "I don't see any reason why it would be" Russian Federation . Yet, while Trump's remarks drew criticism in both parties, the reaction was more muted from the Republican side.
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.
The votes in parliament's lower House of Commons come as Britain's new Brexit minister Dominic Raab heads to Brussels this week for his first talks with the EU's chief negotiator Michel Barnier.
There was a blow for May when a member of her team, defense minister Guto Bebb resigned over the government's acceptance of amendments put forward by Brexit supporter.
Hawaii volcano: Flying lava injures 13 on tour boat
The remaining 9 passengers drove themselves to the hospital, and the Fire Department reported their injuries were not as serious. At least 13 people have been injured after lava smashed through the roof of a tour boat following an explosion in Hawaii.