Officials in Brussels are said to have been shaken by reports that Mr Johnson's senior adviser Dominic Cummings has said it is too late for MPs to block a no-deal break on October 31.
With former Prime Minister Theresa May promising the NHS £20bn a year by 2023, there has been some sceptism over this new cash injection as being "new money".
But Barnier has said the European Union will not renegotiate the divorce deal, or Withdrawal Agreement, including the backstop, an insurance policy to prevent a return to a hard border between the British province of Northern Ireland and European Union member Ireland.
Asked about the potential job losses of Brexit to Scotland, she said that it was hard to predict the outcome, as "nobody has even left the EU".
He was said to have told ministers that, even if the Government lost a vote of confidence when Parliament returns in September, Mr Johnson could delay an election until after October 31 by which time, under current legislation, Britain would be out of the EU. I think it's going to be a very rocky and tumultuous phase that we are heading into, but then after the election; an agreement and a deal will then be struck.
However, he said, they failed to muster the numbers as pro-EU Conservative rebels were cancelled out by pro-Brexit Labour rebels who voted with the Government.
The European Union says its door remains open should British Prime Minister Boris Johnson want to discuss his country's departure from the bloc but it insists that the Brexit divorce agreement can not be renegotiated.
Many critics of May's deal raised concerns over the backstop, which would also involve a temporary single customs territory that would remain unless both parties agreed it was no longer required - a measure that would to all intense and purposes keep the entirety of the United Kingdom in the EU customs union.
But if the future is a no-deal Brexit the staffing crisis may worsen, as the flow of EU-trained staff into the NHS over many years is abruptly reversed: with no staff to work them or in them - even shiny new scanners and buildings are of little use to patients or the NHS.
On Monday, Mr Johnson - in office less than two weeks - travels to Lincolnshire, eastern England, to lay out details of his 1.8 billion pound (S$3 billion) boost for the National Health Service, delivering on his 2016 Brexit campaign vow while maintaining a focus on domestic policies.
Matt Hancock said: "Today we are announcing funding for a new expanded A&E facility at the Pilgrim Hospital". If neither is able to, Mr Johnson might be forced to call a general election.
Mr Hancock said: "I guarantee that we now have all plans in place to make sure that the NHS will be prepared whatever the Brexit scenario".