The National Bus and Rail Union (NBRU) claims it would be "preposterous" if the government allowed the public transport system to collapse due to the pandemic.
CIE has written to the Transport Minister to say it is in serious financial trouble after a big drop in passenger numbers.
According to The Irish Times, Bus Éireann, Irish Rail and Dublin Bus could run out of money as early as next month.
Dermot O'Leary, from the NBRU, says the government must step in.
"The fact that the State would let its own national carrier - which is what CIE is - fail would be untenable," said Mr O'Leary.
"It would be preposterous, I would suggest.
"The one thing that cannot happen is CIE cannot be allowed to fail.
"It is vital and it is significant that transport services supplied by CIE have been the last man standing across this country."
Fianna Fáil TD Marc Mac Sharry has called on the Minister for Transport to provide emergency supports for public transport companies during the current crisis.
"In the current crisis revenue has evaporated. This means some of our semi state public transport companies are in a pathway to insolvency unless the appropriate level of financial support is injected into these companies without further delay," said Deputy Mac Sharry.
"As we look to the future, public transportation has a key role to play in meeting our climate action goals.
"It is therefore vital that we provide all necessary support to our semi state public transport sector at this time and that services continue to run during this public health emergency."