The European Commission president took the hard-line stance as it emerged that EU leaders were considering taking the first steps towards trade and transition negotiations.
The EU has told Britain that a summit next week will conclude that insufficient progress has been made in talks for Brussels to open negotiations on a future trade deal.
But Mr Juncker insisted he is "not in a revenge mood" and "not hating the British", adding: "The Europeans have to be so grateful for so many things Britain has brought to Europe".
"It won't be easy with 28, but with 98 I imagine it to be downright impossible", Juncker said.
"I don't even understand this problem", Juncker said. Let them here, let them there. They have to pay.
In a speech in Florence last month, May said: " I do not want our partners to fear that they will need to pay more or receive less over the remainder of the current budget plan as a result of our decision to leave". "Why are we discussing nonsense like that?"
"Brexit is a serious issue", he said.
The EU says Britain has to make sufficient progress on three divorce issues - the bill, the rights of EU citizens in Britain, and Northern Ireland - before opening the trade negotiations London wants.
On Thursday, Barnier and the U.K.'s lead negotiator, David Davis, said there had been progress on the issue of citizens' rights.
It echoes Mr Barnier's concerns that a "disturbing" deadlock over the size of Britain's exit bill means it is not yet time to move on to negotiations over the future UK/EU relationship.
But the European Commission official did offer some hope by claiming he would explore "ways of getting out of this deadlock" in time for the European Council summit on 14 December.
The Prime Minister also said the United Kingdom would "want to make an ongoing contribution" to any European Union agencies and organisations the United Kingdom remained part of after Brexit - such as Europol.
Shadow Brexit secretary Sir Keir Starmer told the BBC: "The Tories' Repeal Bill is simply not fit for objective".
Meanwhile, an aide to the Treasury's ministerial team dismissed calls by Tory grandee Lord Lawson for Chancellor Philip Hammond to be sacked.
In response to Mr Juncker's comments, Downing St said Mrs May had made clear in her Florence speech that the United Kingdom would honour its financial obligations.
The deadlock in the talks comes despite Theresa May promising to "honour commitments" to the European Union budget made while the United Kingdom was a full member of the bloc.