But shadow chancellor John McDonnell said he believes there is a majority in Parliament to maintain the winter fuel allowance and "triple lock" state pension guarantee, two policies the Conservatives proposed changing in their manifesto. May and her party had been expected to win by large margins, but things did not go as she had planned.
British Prime Minister Theresa May reached an "outline agreement" on Saturday with the ultra-conservative Democratic Unionist Party in order to be able to govern after a humiliating election that has left her authority in tatters. "There's a whole range of issues like that where we think there'll be a majority in Parliament".
The "right leader of the Conservative Party", he claimed, could appeal to German and French presidents for a deal to keep us "within the European family" while addressing immigration concerns. Their core, central message was strong and stable leadership.
But now May's time in Number 10 looks uncertain after the United Kingdom rejected her "strong and stable" election campaign and left the Conservatives short of a majority.
At the start of the campaign, she was enjoying poll leads of 20 points or more over the main opposition Labour Party. And the objective of its campaign seemed to be not to get close even to winning the election but simply to avoid some sort of complete wipeout. We need somebody who can talk and connect with people like Jeremy Corbyn does.
MARTIN: We're seeing that there are calls for Theresa May to resign.
Her party is deeply divided over what it wants from Brexit. From Labour? And is she likely to?
"I think everybody wants to see an agreement in the end that does respect what the British people voted for a year ago - makes sure that our cooperation with Europe continues, our trade with Europe continues, our security cooperation with Europe continues", he said.
He said Britain's neutrality in the province since 1990 had been the "basis for the peace negotiations". Theresa May did not have to call this election.
"We were waiting for the election in Britain, but in the next few days these talks will begin". "I just don't see how she can continue in any long-term way".
"The other parties in Northern Ireland will know that the unionists can pull the plug at any stage and hold the government hostage".
A party spokesman confirmed the resignation of Hill, a combative character who one former colleague said had helped create a "toxic" atmosphere at the heart of the government.
He stressed he did not share their ultra-conservative views on issues such as abortion and homosexuality, which have caused disquiet among many Conservatives.
The 10 DUP MPs could prove crucial in supporting the Conservatives on key votes after Thursday's election saw Mrs May lose control of the Commons.
MARTIN: Well, so clearly there's a lot to talk about.
"Just to be clear, we will act in the national interest".
The new arithmetic of the House of Commons will also makes Brexit negotiations more hard. So what happens now?
"And that means we can look again at what it is we hope to achieve as we leave the European Union - and I want to be involved in those discussions".
Earlier, Ms. May's former head of communications launched a series of vicious attacks on the PM's decision to place so much trust in her 2 Chiefs of Staff and her inability to connect with voters or the rest of the party. We reached him via Skype.
MARTIN: That's Roger Scully.