Business Secretary Andrea Leadsom said if the EU does not compromise on the backstop, the UK will be leaving the EU without a deal on October 31.
Speaking on ITV’s Peston show, the Conservative MP said there will be no backstop, even a time-limited one, in any Brexit deal.
It follows on from Angela Merkel’s conversation with Prime Minister Boris Johnson on Tuesday in which she is reported to have said there will be no Brexit deal with the UK unless Northern Ireland is in the customs union "forever".
“What they are seeking to avoid in Northern Ireland becomes much more challenging,” Ms Leadsom said.
“We have put through a really well-through compromised offer, which let’s be clear Parliament could get behind.
“There were a number of Parliament who have previously been very strongly against Theresa May’s, who are saying they could support this deal.
“Boris Johnson has put together this deal, it’s for the EU to come together to find a way forward with us.”
Mr Johnson's hopes of securing a deal in time for the summit on October 17 and 18 could now rest on a crunch meeting with Irish prime minister Leo Varadkar.
But the EU's chief negotiator Michel Barnier said Brussels had yet to see any "operational, legally binding solution" to the issue of the Northern Ireland backstop.
The Business Secretary said the Government “will abide by the law” when it comes to the Benn Act, which requires Mr Johnson to seek a delay to Brexit if no-deal has been reached.
She added: “We are determined on Friday 31 October regardless of whether there is a deal or isn’t a deal, but our absolute priority is to ensure there is a deal.”
The prime minister has told the Scottish courts he will write a letter to Brussels, seeking a delay, but reportedly will write a second letter, saying he personally does not want a delay.
Ms Leadsom responded whether it was an appropriate response: “It’s quite clear, the Government’s policy that we not want a delay.
“It’s perfectly reasonable to make that point very clearly…to the EU.
“Boris Johnson is determined to get Brexit done by 31 October.”
While former Conservative MP and London Mayoral candidate Rory Stewart was asked whether Mr Johnson was a good Mayor or a bad Mayor, Rory Stewart said: "He was a big personality."
He added: "To be honest the best Mayor we had in London was from 2000 to 2004, an Independent Mayor of London, he was the one who got stuff done, he was the guy who sorted out the Olympics, sorted out the Oyster Cards."