Sir Jeffrey Donaldson, MP for Lagan Valley, has warned Mrs May that he and the other nine DUP lawmakers propping up her government cannot support her Brexit deal in its current form.
He confirmed his party, whose MPs guarantee Mrs Mays working majority of 13, would not vote for her withdrawal agreement in the House of Commons, dealing a blow to her chances of parliamentary approval.
His comments comes as the Prime Minister prepares to meet with senior cabinet ministers to discuss the draft Brexit deal agreed by UK and EU negotiators.
Donaldson, claimed the deal would “leave Northern Ireland behind” and compromise the constitutional integrity of the UK, making its break-up more likely.
"From what we have seen and heard we do not believe this deal is the best deal," Donaldson told BBC Radio.
"This deal has the potential to lead to the break-up of the United Kingdom and that is not something we can support."
BREXIT DISQUIET: Jeffrey Donaldson said the DUP is not prepared to support the deal (Pic: DS)
LIFE SUPPORT: Donaldson is one of 10 DUP lawmakers who props up May's government (Pic: GETTY)
Donaldson said that, if the PMs Brexit deal does not secure parliamentary support, the DUP does not fear a general election – a possibility in that scenario.
He said: "It's not about who is prime minister, it's not about who governs the country, it's about the constitutional and economic integrity of the UK, that is fundamental for us.
"And it is not just us, the DUP does not stand alone on this, we have many friends within the Conservative Party and indeed in some other parties, who believe this deal has the potential to lead to the break-up of the UK.
"That is not something we can support."
He added that, if Northern Ireland is detached from the UK in any way, Scottish nationalists may use it as a pretext to demand an independence referendum.
“The problem is this fundamentally undermines the constitutional and economic integrity of the United Kingdom,” Donaldson, chief whip of the DUP in Westminster, said.
“If it wants to get out of this binding agreement then it will have to leave Northern Ireland behind … and that will inevitably put pressure on Scotland.
“The Scottish Nationalists will use this deal to pursue their agenda of an independent Scotland.”
NOT ACCEPTABLE: Donaldson said the deal would leave the EU too closely aligned with the EU (Pic: GETTY)
“That is not something we can support”
Hardline DUP MP Sammy Wilson reiterated Donaldsons disavowal of Mrs Mays proposed deal, calling it a “humiliation” for the UK.
"All of the great and the good who were rolled out during the EURef (EU referendum) will be rolled out again in the coming weeks to try and get us to fall into line. We are clear – we will not be voting for this humiliation!" Sammy Wilson said on Twitter.
DUP deputy leader Nigel Dodds also criticised the draft divorce agreement – details of which emerged in media reports on Tuesday – but said the party would wait and see the actual text before deciding if it will vote against it.
D-DAY: Theresa May will today present her Brexit deal to cabinet (Pic: GETTY)
Meanwhile, Former UKIP leader Nigel Farage said he believed the draft plan is "the worst deal in history".
He told ITV's Good Morning Britain: "We're giving away in excess of £40 billion in return for precisely nothing. Trapped still inside the European Union's rule book, continuing free movement of people, continuing with a foreign court having a say over our own country. Nothing has been achieved other than giving away a huge sum of money."
He described Mrs May as "not just the worst prime minister I've ever seen but perhaps the most dishonest one as well".
He added: "Get rid of her. Let's get somebody else, let's come back to the EU and say 'look, let's have a simple free trade deal or we are leaving on WTO (World Trade Organisation) terms'. And do you know what? They'll bite our arms off."
Asked what he thinks will happen next, he said: "I believe that the Cabinet will collapse, I believe that Parliament will collapse. I think we have a career political class who will put their own reselection within their parties above the interests of the nation and our democratic system."