The National Bus and Rail Union (NBRU) says the transport bodies run by the State "cannot be allowed to fail".
It comes amid reports that State funding for Irish Rail, Bus Éireann and Dublin Bus could run out as early as next month.
The Irish Times says the board of the CIÉ group of companies has advised Transport Minister Shane Ross in a letter that they are facing a very serious financial position because of plummeting passenger numbers caused by the coronavirus pandemic.
NBRU general-secretary Dermot O'Leary says these businesses must be kept afloat.
"It was my understanding because of the severe reduction in the amount of people travelling... that is causing problems for the CIE companies.
"But the fact that the State would let its own national carrier - which is what CIE is - fail would be untenable, would be preposterous I would suggest.
"The one thing that cannot happen is that CIE cannot be allowed to fail.
"It's vital - and it's significant I suppose that the transport services supplied by CIE have been the last man standing, practically, across this country."
He also said there needs to be a conversation around the larger transport sector.
"Expressway is unique in that it's alleged to be a commercial service run by Bus Éireann.
"But that Bus Éireann service has links into every nook and cranny, every community in this country and it serves in fact over 40 hospitals.
"[It] has been used over the last number of weeks to convey vital health workers and retail workers to their place of work.
"And there needs to be a conversation in relation to the whole transport sector on completion of this crisis, whenever that it."
"And the notion that Expressway can continue to operate as a commercial operator needs to be addressed in that debate".
He also expressed concern of the position of the Government
"What concerns us in the middle of all this - apart from the issue around Expressway - is that there is no actual Government in place.
"And leaving the decision on transport to a failed general election candidate, which is what Shane Ross now is... is also unacceptable".