The Government's main concerns centred on the Progressive Unionist Party and Ulster Democratic Party, the small groupings which speak for the main loyalist paramilitary groups.
Yesterday neither was giving guarantees that they would be at the multi- party talks when they resume next Monday at Stormont following the Christmas break. The general fear is that the withdrawal of even one of them from the talks could lead on to a breakdown of the loyalist ceasefire.
The Government is also anxious to keep the largest party, David Trimble's Ulster Unionists, at the Stormont table. Mr Trimble yesterday met Tony Blair at Downing Street for talks which both sides described as constructive.
As the political activity continued, Catholic Belfast buried the latest of its dead, 31-year-old Eddie Treanor, who was shot dead in a loyalist attack on a bar in the north of the city on New Year's Eve. At his funeral, the Catholic bishop of Down & Connor, Dr Patrick Walsh, appealed to politicians to work together, adding: "Do not dispirit us any further with petty shows of rancour, bitterness and ill-temper. There is so much at stake. Lives are at stake. Every single life is precious."
Reports persist that the Ulster Defence Association, which is one of the elements involved in the talks, was behind the shooting. On Sunday, a majority of UDA members held at the Maze prison voted to withhold their support from the peace process, though it was said this did not mean they favoured ending their ceasefire.
The UDA leader in the jail, Sam McCrory, said: "We want to send a clear message to the Government that we don't want to play second fiddle to Sinn Fein-IRA or any republicans. If they're going to give any concessions to republicans they have to give them to loyalists also."
David Ervine, who is leader of the Progressive Unionist party which has links with another paramilitary group, said after meeting Dr Mowlam: "I'm not talking about breaches or collapses of the ceasefire. I'm talking about a process that needs fixed. If it is not fixed it will run into the sand."
His colleague, Billy Hutchinson said not enough had emerged from the meeting for him to attend the talks next week, adding: "She has got until the end of the week to prove she is going to make changes."