The Higher Education Minister recently ruled out striking a deal to garner the support of Independent TDs.
Midlands Independent TDs are at odds over whether to support Simon Harris.
The Government holds a slim majority, but can typically rely on some of the Independents to bolster support in votes.
Roscommon Galway TD Denis Naughten says he'll be voting for Minister Harris as Taoiseach, after working with him in the past on flooding, health and science issues.
However, Laois Offaly Deputy Carol Nolan says nothing short of an asteroid will prevent her from opposing the Higher Education Minister's campaign.
Kildare South's Cathal Berry is yet to make a formal decision on the matter.
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