Senators were due to return to work on 18 September.
The campaign, initiated by Senator Daly, is seeking to get Minister for Health James Reilly to annul legislation arising from an EU regulation.
Fianna Fáil leader of the Seanad Senator Darragh O’Brien said Mr Reilly signed the EU directive into law without any consultation or scrutiny by the Dáil or Seanad.
He said the party had had 110 sitting days to seek an adjournment debate, adding that more recently Fianna Fáil did not avail of eight opportunities to raise it in Private Members’ Time.
Independent Senator John Crown called for speedy legislation to plug the holes in the existing transplant services.
He said Ireland has a serious issue with heart disease, yet only has one twenty-fourth of the heart transplant rate of the leading transplant country in the world.
The Government parties are opposing the motion, arguing that it would be illegal to annul the directive in the absence of a recommendation from the Oireachtas European Affairs Committee.
Today’s vote could be close, but Government sources say they are confident the motion will be defeated.
Despite some criticism of the recall, there was some common cause across the political lines that if nothing else today’s proceedings may at least have raised the profile of the issue of organ donation.