After the disastrous Tory showing in the General Election left the party eights seats short of a majority, the Prime Minister has made a sustained effort to woo the 10-strong bloc of DUP MPs ahead of crunch votes this week.
The uncertainty surrounding the Prime Minister's position is also being fuelled by speculation the Tories may soon be thrown into a leadership contest.
The DUP has made it clear it will only agree a deal if it delivers tangible benefits for Northern Ireland in terms of jobs and investment in health and education.
Labour has insisted that any financial sweeteners offered to Northern Ireland as part of an agreement must be made fully public.
The potential hook-up has also caused concern among some Conservatives.
Tory grandee Lord Chris Patten said: “The DUP is a toxic brand and the Conservative Party has got itself back into the situation where there's a danger of it looking like the 'Nasty Party', to borrow from Theresa May.
“Every vote will cost you. Every vote, you will have to find some way of paying for it and then explain to the Scots and the Welsh and people in the North East why they can't have the same thing too.”
Amid reports of Tory MPs seeking a replacement for Mrs May, International Development Secretary Priti Patel refused to deny she would run for the party leadership in the future, and Brexit Secretary David Davis side-stepped a question on his own ambitions.
Mr Davis cautioned that a leadership contest would have a “catastrophic” impact during Brexit negotiations.
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