Monaghan councillors say it would be a "travesty" if no further funding is forthcoming for the N2 Clontibret to the Border scheme.
It was one of a number of projects to be stalled by the TII in January, and councillors have renewed a request to the Taoiseach for funding.
Monaghan councillors say the N2 Clontibret to the Border project has been "shelved" and "terminated" after it was recently stalled by TII.
However, the Ardee to Castleblayney part of the scheme remains on track after a one million euro allocation.
At February meeting with local Minister Heather Humphreys, Monaghan councillors were told it would cost around €3 million to complete the phase 3 design process in 2022 or 2023.
It was warned that an extended delay will increase costs and may require work to be repeated.
The possibility of accessing Shared Island funding was discussed, but the Council is still awaiting a response from the Taoiseach in relation to this.
At this week's County Council meeting, Brian McKenna said the lack of response is "disappointing" and said "it would be worthwhile renewing this request" for €3 million from the Shared Island fund.
He added that "time is not on our side, so we need an answer one way or another."
Meanwhile, Paudge Connolly warned that extra funding is "needed to protect the money already spent".
He told the Chamber a "positive response is needed" and added that it "would be a travesty to lose progress made here".