The three parties who are trying to form the next government are under pressure to get their individual party votes over the line by next Friday.
There are two important pieces of legislation that need to be passed by the full Oireachtas by the following Monday, 29 June: the renewal of the Offences Against the State and the Criminal Justice Acts.
Due to their exceptional nature, both are renewed each year by the end of June through a motion in both the Dáil and the Seanad.
What is so special about these two laws?
The Offences against the State Act (1939) was amended after the Omagh bomb in August 1998 in which 29 people were killed.
There are anti-terrorism provisions within the law that include it being an offence to direct an unlawful organisation and train people in the making and use of firearms.
Last year when he argued in the Dáil for the renewal of the act, Minister for Justice Charlie Flanagan spoke of the garda assessment that there was "a real and persistent threat from republican paramilitary groups" on the island of Ireland, and he referred to the killing of journalist Lyra McKee in Derry in April that year.
The Criminal Justice Act 2009 introduced additional measures targeted at combatting organised crime.
Mr Flanagan last year spoke of the "pernicious nature" of the activities of serious organised criminals in Ireland and reminded the House of the many murders that had been carried out, particularly in residential areas of Dublin.
Both laws provide for certain offences to be tried in the Special Criminal Court. The court sits with three judges and no jury, in order to avoid jury intimidation.
When will they be renewed?
On Wednesday morning, the Dáil is due to hear the motion to renew these laws. A debate and a vote will follow.
If the motion is passed in the Dáil, then the Seanad should sit to debate and pass the renewal of both laws.
However, the Seanad has not been sitting, because it does not have its full compliment of 60 Senators.
That is due to the nature of the election and nomination of the Upper House.
Forty-nine Senators are elected from a variety of panels; the election of those was completed in the first week of April.
The remaining 11 Senators are nominated by the incoming taoiseach.
It is expected those nominees will be named swiftly once a taoiseach is voted in.
Why are Senators going to the High Court?
Some Senators argue the Seanad should be sitting already, and they are going to the High Court to argue their point.
A group of ten Senators, led by Labour's Ivana Bacik and independent Michael McDowell, say it is within the Taoiseach's remit to ask the President to allow the Seanad to sit without the 11 nominees.
In a letter to the group on 10 June, Taoiseach Leo Varadkar said the Constitution did not allow him to do that, but he agreed it was an important point of law that he said "needs to be clarified due to the fact that necessary legislation may need to be enacted in the coming weeks".
The hearing in the High Court is scheduled for Wednesday morning. Senator Bacik believes there could be a decision given by Thursday or Friday and if in their favour it would allow the Seanad to sit without delay.
What would happen if the laws didn't get renewed?
There is a possibility the Seanad won't sit, the programme for government doesn't get through the three-party vote, and therefore the renewal of the legislation is delayed.
If that happens, there are certain sections of the laws that may have an adverse effect on the Special Criminal Court.
Senator Bacik, who has practised as a lawyer in the Special Criminal Court, says it will still exist and sit for certain offences to be heard.
However, she says, An Garda Síochána may be severely hampered in investigations due to certain provisions lapsing such as, if an accused refuses to talk, gardaí would no longer be able to make inferences about that silence, and the extension of detention and rearrest would not be permitted.
Senator Bacik says these are very strong tools used by gardaí in these serious investigations, which, if no longer allowed, could put significant obstacles in the way for the prosecution of offences.