Fine Gael leader Leo Varadkar told his parliamentary party last night that he is confident a new government can be in place by June.
He said he was determined that any coalition would last four to five years.
However, what is described as a considerable number of his TDs and senators sought reassurances over coalition policy, with Minister for Agriculture Michael Creed expressing particular concern at the 7% emissions reduction target.
Minister for Finance Paschal Donohoe has said it is certainly possible to form a government by the end of this month and it will be needed to introduce taxation arrangements to support businesses.
Speaking on RTÉ's Morning Ireland, Mr Donohoe said that legislation will be required "in particular for taxation arrangements" and if there is a government formed by June he can bring in legislation that employers need.
Mr Donohoe said his party are entering negotiations tomorrow in "best faith and with its best foot forward", although it will be challenging.
He said any programme for government agreed must get the balance right between "recognising the reality we now face as a country" while also striving and delivering on aspirations we still have as a country.
He said nobody involved in the process wants another election and it is incumbent on politicians to put together an affordable programme for government.
Responding to the negotiations between Fianna Fáil, Fine Gael and the Greens, People Before Profit has written to Sinn Féin suggesting that parties on the left should renew their efforts to create what it terms "an alternative programme for real change".
Meanwhile, the Dáil has returned today for statements on tourism and childcare, as well as to establish a new Dáil committee to focus on the Covid-19 crisis.
This special Dáil committee will have 19 members - four seats each for Fianna Fáil, Sinn Féin and Fine Gael, with one seat each for the other parties and Independent groupings.
Unusually, it is meeting in the Dáil chamber to comply with physical distancing.
The Labour Party, which called for an all-party Covid-19 committee at the end of February, said it was happy that both the Taoiseach and Minister for Health Simon Harris would appear before the body.
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Meanwhile, Mr Donohoe has said that changes to the way the Temporary Wage Subsidy Scheme to make sure it is more effective for those on lower incomes are being made today.
Mr Donohoe said the wage subsidy scheme is keeping over 400,000 people in a job which is critical.
He said that pandemic welfare payments are going to continue in a form but the level of payment and what form they will continue in will be decided on soon.
He said the supports are working to keep people in a job and to cope with a huge change in living standards.
However, he said that the payments are costing many hundreds of millions each week and will be changed in a way that is affordable but also makes sense to our citizens.
He said that he is absolutely confident the country can rise to and overcome the current challenges to national finances and to the numbers of job losses.
He said the forecast deficit could rise beyond €23 billion depending on the success in overcoming the public health challenge.
Speaking on the same programme, Sinn Féin's finance spokesperson Pearse Doherty said he does not believe ordinary families should suffer tax increases as a result of the pandemic.
Mr Doherty said that the economy was put to sleep to try and prevent deaths and the burden of recovery cannot be put back onto workers.
He said that Sinn Féin was concerned this might happen because the government have made it clear that they will obey the fiscal rules "slavishly".
Mr Doherty said we need to insure that there is liquidity in households and businesses.
Separately, Social Democrats co-leader Roisín Shortall has said there has been a democratic deficit in the handling of the Covid-19 crisis and the opposition have been frustrated by the lack of opportunities to debate the handling of the crisis with the Government.
Also speaking on RTÉ's Morning Ireland, Ms Shortall said while there have been regular online briefings, that is very different to engaging with a minister and there are a a whole range of issues that need to be addressed.
Ms Shortall welcomed the fact that, from today, the Dáil will sit for two days a week.
Ms Shortall said health officials have made themselves available for daily briefings with the media but this opportunity has not been available at a political level and it was important that they made themselves available for engagement.
She added more constructive work can often be done at a committee setting.
