The Regional Technical Group is making the call.
A number of midlands TDs are among those calling for a vote for Taoiseach at the next Dáil sitting.
The vote will take place on March 19th, at the request of the Regional Technical Group - which includes independent TDs, Cathal Berry from Kildare-South and Roscommon-Galway's Denis Naughten, along with Aontú leader, Meath-West deputy Peadar Tóibín.
Deputy Naughten says they hope this two week deadline will help focus the minds of the main party on the urgent need to form a stable and effective government.
He says the public is losing patience, four weeks on since the first inconclusive vote for Taoiseach: