Gail Cartmail, Unite assistant general secretary, said Carillion's workforce was being "held hostage by the whims of the market".
The Government is notoriously slow at settling bills with contractors, and frequent delays have exacerbated Carillion's cash crunch. "The collapse of Carillion could provoke a serious crisis".
"The Government can't just do a financial bailout".
Carillion is behind large government infrastructure projects including the HS2 high-speed rail, but the firm is grappling with £1.5bn of debt and a pension shortfall of £587m.
He told the BBC: "I think what has to happen in this case is the contracts have to be kept going and supporting the supply chain and the tens of thousands of workers and that can be done by the Government taking a lot of this in-house or re-tendering in other cases".
In addition to its rail operations, Carillion also manages almost 900 schools, provides services to the NHS and works with National Grid.
Adding to the pressure on the small cap firm - which issued three profit warnings in less than six months past year and has seen its market value collapse by 90% - was a recommendation from broker Peel Hunt to sell the stock ahead of forthcoming newsflow.
The company is seeking financial support from commercial lenders or the government to avoid being put into administration.
He said it was a "pretty messy situation", adding: "The situation is pretty bleak". The long-awaited route is due to be finished this year following lengthy delays.
Carillion is holding crisis talks with United Kingdom government representatives on Friday, which Sky News said were aimed at safeguarding the more than 28,000 pension scheme members who face potential cuts to retirement payments should Carillion fail.
The meeting comes as Carillion - a major government contractor on projects including High Speed 2 - races to secure additional funding to avoid collapse, with around 19,500 United Kingdom jobs at risk.
In a statement, Carillion said: "Suggestions that Carillion's business plan has been rejected by stakeholders are incorrect".
Senior ministers met on Thursday to discuss the future of construction giant Carillion, amid fears the struggling firm is approaching collapse.
"As part of its engagement with stakeholders, Carillion is in constructive dialogue in relation to additional short term financing while the longer term discussions are continuing".