Parties in Northern Ireland reacted to the Downing Street developments with renewed calls for an election.
The SDLP blamed what it called the "problem parties" for "messing around".
Mr Alban Maginness said: "It is no surprise that people on the ground are frustrated and angry. People are looking at the UUP and Sinn Féin and wondering if they are really up for the agreement because neither party has yet signed up in full to the Joint Declaration.
"Sinn Féin has not met its requirements on ending paramilitarism and the UUP has not yet signed up on normalisation and working the institutions."
However, the former Assembly member added: "But there is still enough time to get this sorted if the problem parties want to get it sorted. The impasse can still be broken. But come what may, it is time to go back to the people and let them deliver their verdict on who is working the agreement and who is not. There should be no more delays. There must be elections now."
The Women's Coalition also called for decisive action from Downing Street, whether or not there is a positive outcome from the talks. Ms Jane Morrice said the public needed more than political rhetoric or skilful negotiation if confidence was to be restored.
She said: "Again, politicians face a crunch time, but unlike key moments over the past year, this time we cannot let a resolution slip through our fingers.
"It's not enough to talk about how much parties want a positive outcome - they need to make a positive contribution to bring that about. From the IRA, we need a decisive statement and action on decommissioning; from the Ulster Unionists, a commitment to come back into executive and be part of a collective implementation process; from the governments, we need a firm commitment to democracy in Northern Ireland. We are concerned that a tête-à-tête process with selected parties has not resulted in workable solutions before."
The DUP accused Mr David Trimble of having the Assembly elections cancelled because he talked the British Prime Minister into fearing the outcome.
A former Lagan Valley Assembly member, Mr Edwin Poots, said: "He has no mandate to traipse off to London and negotiate away Northern Ireland's future on the basis of the Joint Declaration."
He added that the declaration would provide an amnesty for on-the-run paramilitaries, destroy the Royal Irish Regiment, allow the Republic a greater say in Northern Ireland affairs, and hold out the prospect of a Sinn Féin justice minister at Stormont.
Mr Poots asked: "Can we really expect the man [Mr Trimble] who acquiesced to the early release of terrorist prisoners, the effective disbandment of the RUC and unaccountable all-Ireland institutions to carve out a better deal for unionism at this time?" Mr Trimble's mandate had run out, the DUP said. "He is not entitled to speak for unionism anymore."