Fianna Fáil's determination to pursue plans to build private hospitals on public hospital grounds is a major obstacle in the effort to form a coalition with the Green Party.
Following the third day of talks between the parties in Government Buildings, which are now scheduled to end by tomorrow, both sides said that progress had been made.
However, Minister for Social and Family Affairs Séamus Brennan acknowledged that the opposing positions on hospital co-location, with Fianna Fáil and the Progressive Democrats in favour and the Greens against, have not edged closer.
"The health area is one area that we have still to make some good progress on. We are still in the middle of that," he said after the end of nine hours of negotiations.
Papers on contentious issues have been exchanged by the negotiating teams, though they have yet to discuss Fianna Fáil's desire to cut both the standard and top rate of tax.
Asked if he believed the parties could strike a deal, Mr Brennan said: "I believe we can. Am I certain? No, but I believe that we can. Both sides have entered these talks in good faith.
"The atmosphere is cordial and constructive. We should be able to get there, but it is a cautious prediction on my part that we will get there.
"We made good solid progress. There are still issues which we have only touched on that are quite substantial. We are moving those issues on gradually," he added.
Confirming that a deadline of tomorrow had been set for conclusion of the talks, he said: "We are working to a time-frame. The Greens have a conference on Sunday. They have that pressure point."
Fianna Fáil is opposed to the Greens' demand for a carbon tax, on the ground that it would be punitive for industry, although a long-term review could be promised.
The Fianna Fáil negotiating team is led by Minister for Finance Brian Cowen and includes Minister for Communications Noel Dempsey.
The Green Party delegation, led by deputy leader John Gormley, includes former Cork South Central TD Dan Boyle and the party's general secretary Dónall Geoghegan.
If a package is agreed, it will be put to 800 delegates at the Green Party's Mansion House meeting.
Although the Green leadership has imposed a gagging order on its members, it is understood there is disquiet among some members about the prospect of an alliance with the Progressive Democrats.
Taoiseach Bertie Ahern has kept the PD acting leader and Minister for Health, Mary Harney, informed of developments. She will attend a Cabinet meeting today along with the Minister for Justice, Michael McDowell, who lost his seat.
Senior Fianna Fáil sources insist that Mr Ahern and his party are determined to strike a deal with the Greens, the PDs and Independent TDs, Beverley Flynn, Jackie Healy-Rae and Michael Lowry.
During negotiations the Greens have also been pushing for a pupil-teacher ratio of 25-to-one and much greater availability of specialist applied behavioural analysis (ABA) teaching for autistic children.
Fianna Fáil is willing to accept local government reform which is also being sought by the Greens, including the possibility of directly-elected mayors, sources close to the talks told The Irish Times.
It has also expressed a willingness to consider a review and potential moratorium on municipal incineration, but on the basis that it could not apply to plants with current planning approval, or those in the middle of the planning process.
The incineration company Indaver has put plans to build incinerators in Meath and Cork Harbour on hold because of unhappiness over Government policy, while a third planned incinerator for Poolbeg in Dublin Bay has also run into difficulties.