The DUP - whom the Prime Minister relies upon to prop up her Government in a so-called "Confidence and Supply" deal - has ramped up their rhetoric against the Government, with threats to vote down any deal that compromises the integrity of the Irish border.
"This will not be an agreement at any cost", the PM added.
"I believe a referendum will happen as people come to the conclusion that since 2016 the situation has changed and at some point they will want to have the final say", said Brown in a speech this week.
Downing Street said that reports that Brussels' chief negotiator Michel Barnier expected the "parameters" of a deal to be presented to ministers for approval at their regular weekly meeting should be taken "with a bucket of salt".
The amendments to the Finance Bill, drafted by MPs Chuka Umunna and Anna Soubry, two leading supporters of the People's Vote campaign, would force the Treasury to carry out and publish an impact study of any Brexit deal before MPs have a "meaningful vote" on leaving the EU.
"We want an agreement to be reached as soon as possible but urgency is required". He said he hoped the Prime Minister would keep her promises. International Development Secretary Penny Mordaunt told Sky News on Monday that the cabinet would be a "check" on the deal.
"Cabinet's job is to put something to Parliament that is going to deliver on the referendum result".
Facebook outage impacts thousands across US
The outage, caused by a test the social network was conducting, lasted about 40 minutes. A check of DownDetector showed Wichita's outage was minor compared to the East Coast.
Officials from both sides were engaged in talks in Brussels which began on Sunday and lasted until 2.45am on Monday but failed to produce a decisive breakthrough.
While officials choreograph the biggest divorce deal in European Union history, it remains unclear whether May can get a deal through parliament, where opponents have said she is betraying Brexit by signing up the United Kingdom to European Union subjugation.
The main battle remains over the Irish backstop, which would prevent the return of a hard border on the island of Ireland by allowing all of the United Kingdom to remain in a customs union after the post-Brexit transition period ends in December 2020.
The stinging attack comes ahead of a Cabinet meeting on Tuesday, with Johnson saying that Mrs May's plan would reduce the United Kingdom to the status of a colony.
But ministers emerging from the meeting did little to encourage expectations of an early resolution.
However, with the negotiations now down to the most hard issues, he said that there had to be a "measure of caution".
"The two teams have really intensified their engagement", Coveney said afterwards.
"And we support his efforts to continue working towards a deal", he added. But Austrian EU affairs minister Gernot Bluemel, whose country holds the EU's rotating presidency, said "so far progress is not sufficient to call in and set up another (summit)".
On the other side of the debate, there's growing criticism of May among pro-EU Conservatives, with the shock resignation of Jo Johnson as transport minister on Friday triggering speculation that others could follow. Others on the Remain side are concerned that Britain would be a rule-taker without a say on a major chunk of economic policy.