Theresa May should "rethink her reckless red lines" and consider remaining part of the customs union and single market, Labour has urged.
Shadow Brexit secretary Sir Keir Starmer said there needed to be a UK-wide response to Brexit, after the Democratic Unionist Party refused to accept proposals on a customs border, leading to a deadlock in talks.
But Brexit Secretary David Davis said Labour's policy on the customs union and single market had changed "10 times" in the last year.
Sir Keir, who asked an urgent question in the Commons on the negotiations, said: "Labour is clear that there needs to be a UK-wide response to Brexit.
"So the question for the Government today is this: will the Prime Minister now rethink her reckless red lines and put options such as a customs union and single market back on the table for negotiation?
"Because if the price of the Prime Minister's approach is the break-up of the union and reopening of bitter divides in Northern Ireland then the price is too high."
Mr Davis pointed to comments made by members of the shadow cabinet on remaining in the single market and customs union, and said: "So much for Labour policy on this matter, we can see why it's changed 10 times in the course of the last year."
He continued: "The suggestion that we might depart the European Union but leave one part of the United Kingdom behind still inside the single market and customs union - that is emphatically not something that the UK Government is considering."
Mr Davis said the Government was in the middle of an "ongoing round", and that, while progress had been made, a final conclusion had not yet been reached.
"I believe we are now close to concluding the first phase of negotiations and moving on to talk about our future trade relations," he said.
"There is much common understanding, and both sides agree that we must move forward together."
He told MPs the Government had always been clear that it wanted to protect "all elements" of the Good Friday Agreement to "maintain the common travel area and to protect associated rights".
Mr Davis said the Government recognised that the "integrity" of the EU single market and customs union must be respected after Brexit, but added that it was "equally clear we must respect the integrity of the United Kingdom".
But Sir Keir claimed the last 24 hours had given a "new meaning to the phrase 'coalition of chaos'".
"It's one thing to go to Brussels and fall out with those on the other side of the negotiating table; it's quite another to go to Brussels and fall out with those supposedly on your own side of the negotiating table."