A No 10 source says a Brexit deal is "essentially impossible" after a call between the PM and Angela Merkel.
Boris Johnson spoke to the German chancellor earlier about the proposals he put forward to the EU – but the source said she made clear a deal based on them was "overwhelmingly unlikely".
They also claimed she said a deal would never be possible unless Northern Ireland stayed in a customs union.
Mrs Merkel's spokesman said they did not reveal confidential conversations.
The President of the European Council, Donald Tusk, sent a public tweet to Mr Johnson, writing: "What's at stake is not winning some stupid blame game. At stake is the future of Europe and the UK as well as the security and interests of our people."
Ireland's Tánaiste (Deputy Prime Minister), Simon Coveney, tweeted it was "hard to disagree" with Mr Tusk, adding: "We remain open to finalise a fair Brexit deal, but need a UK government willing to work with EU to get it done."
Scotland's First Minister and leader of the SNP, Nicola Sturgeon, said Downing Street's response to the phone call was an "attempt to shift the blame for the Brexit fiasco", while Labour called it a "cynical attempt to sabotage the negotiations".
Shadow Brexit secretary Sir Keir Starmer said Mr Johnson "will never take responsibility for his own failure to put forward a credible deal", and called on Parliament to "unite prevent this reckless government crashing us out of the EU".
Officially, the prime minister's spokesman said talks with the EU were "at a crucial point", but denied they were over./BBC news