The Conservative leader is still trying to thrash out the terms of a coalition with the party, with the Queen's speech, which signals the state opening of parliament now delayed by two days until Wednesday June 21.
At a rally in Sheffield, protesters including Labour supporters held up placards saying "we've been DUPed".
Sources told the BBC any public statement about the talks yesterday would have been seen as inappropriate after the Grenfell Tower tragedy.
"There is an irony to being lectured by some about our role in the national government of the United Kingdom when Sinn Fein want to be in government here in the Republic of Ireland", she said.
"The power-sharing institutions collapsed because of the DUP's RHI financial scandal and the refusal of previous Tory governments and the DUP to implement previous agreements".
A truly neutral guarantor "has in fact never been the reality, but now even this pretence will be dropped", said Emma Clancy, a political adviser for Sinn Fein. Other politicians have voiced their concern as well.
The person referenced is Gerry Adams, president of Sinn Féin.
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Speaking on The View programme on Thursday night, Mr Smith said he sensed a "willingness" among the parties to come to an agreement before the deadline on 29 June.
By forming a government with the DUP, many commentators have argued the Conservatives would undermine this arrangement and risk the peace process.
It could "catapult Northern Ireland into a serious crisis and back onto our front pages", he wrote.
Sir John Major is one of those urging caution. "It's not certain, it's under stress, it's fragile".
Penned by the former deputy first minister at the time of his January resignation from Stormont, it mapped out obstacles to power-sharing in Northern Ireland. But there is no possibility that she will pull out of the still, not over the line deal with the DUP, required by her to form a government.
The new landscape is a belated outworking of the two governments" strategy of cultivating the DUP and Sinn Fein, rather than parties that were, at the time, considered "centre ground'.
Referring to financial controversies which helped tumble the Executive earlier this year, including the Cash for Ash scandal linked to Ms Foster, Mr Kearney said they continue to overshadow the region.
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