She also faces the prospect of an internal rebellion over Britain's withdrawal from the EU's nuclear oversight treaty, and to cap it all, her infrastructure adviser Andrew Adonis warned on Friday that quitting the customs union and single market would be an error on the same scale as the British decision to appease Adolf Hitler before World War II.
"If it were to take that position and we were to do a hard Brexit then I do believe this would be the worst mistake this country has made since 'appeasement' in the 1930s and it will impoverish millions of working people," Adonis told BBC radio on Friday.
May "completely disagrees with" Adonis, her spokeswoman, Alison Donnelly, told reporters.
Stripped of her majority by last month's election, the premier is relying on party loyalty and 10 lawmakers from Northern Ireland's Democratic Unionists to get her agenda through the House of Commons.
"The future of this country is being held back because we have a weak or no government in power at the moment," the opposition Labour Party's finance spokesman, John McDonnell, told BBC TV late on Thursday.
"This government's falling apart rapidly and I think the Conservative party is split in about five different ways."
Brexit Negotiations resume on Monday in Brussels amid signs May's government is willing to make concessions on previous hard-line positions.
Davis told the BBC on Thursday that the UK may seek associate membership of Euratom, amid a rebellion within his own Conservative Party over plans to pull out of the nuclear oversight organization. This may be thwarted by the government's intention to end the European Court of Justice's jurisdiction in the UK and freedom of movement.
The statement on the bill contrasted with the more bellicose tone used by Foreign Secretary Boris Johnson this week. Answering questions in Parliament, he agreed with euro-skeptic Tory lawmaker Philip Hollobone who suggested the foreign secretary should "make it clear to the EU that if it wants a penny piece more" from Britain as part of the Brexit settlement, "it can go whistle."
Johnson responded that "the sums that I have seen that they propose to demand from this country seem to me to be extortionate, and I think that to 'go whistle' is an entirely appropriate expression."
EU chief negotiator Michel Barnier said in response that "I am not hearing any whistling, just a clock ticking" down to Britain's March 2019 withdrawal.
"We will need to discuss a fair settlement of rights and obligations," Donnelly said. "We have always said there may be specific programs we may want to continue to contribute to once we leave."
Luxembourg Prime Minister Xavier Bettel said on April 29 that the sum would be between 40 billion euros and 60 billion euros. EU negotiator Michel Barnier hasn't publicly endorsed a number and argued he is only asking the UK to cover financial commitments it made as member of a bloc, which may extend beyond 2019.
While the language of the statement is dry, it's the first time Britain has said in writing that it accepts the need to pay a financial settlement. In the past, some officials have questioned whether the UK has any legal obligation to pay anything.
When May wrote to European Council President Donald Tusk in March to officially trigger two years of Brexit talks, she referred to it obliquely, saying "we will need to discuss how we determine a fair settlement of the UK's rights and obligations as a departing member state."
While the issue is political dynamite, the UK's Office for Budget Responsibility said on Thursday that the bill is unlikely to "pose a big threat" to the government's finances.
