The warning from unions and opposition politicians comes amid speculation about the future of Jarvis, involved in 19 PFI deals covering more than 120 schools.
Its share price of the firm, which recently accepted blame for the Potter's Bar rail crash, has fallen from pound;3.60 to 23.5p in less than a year.
It has debts of pound;230 million.
Vincent Cable, Liberal Democrat Treasury spokesman, has called on Education Secretary Charles Clarke to say what will will happen to schools if Jarvis goes bust.
PFI deals usually cover facilities management and building work and can last for up to 30 years.
A Department for Education and Skills spokeswoman said: "While PFI procurements are the responsibility of the local authority, the DfES maintains close contact with councils throughout the process and monitors the progress of projects after contract signature has been reached."
It is understood that the banks which lend to PFI projects would be expected to step in and find an alternative contractor to finish the work, but it is unclear how long that process would take.
Public Risk for Private Gain, a report from the public-sector union Unison, a long-time opponent of PFI, said the Government has been forced to step in to bail out previous projects. Taxpayers were left with a bill for pound;12.6m when a passport agency deal with Siemens went wrong, it said.
The union said that the "complex and secretive nature" of PFI deals made it hard for schools and outside observers to predict what would happen to individual projects.
Dave Prentis, Unison general secretary, said: "The public has a right to know that money is being spent wisely. The Government must carry out an inquiry into all PFI schemes as a matter of urgency."
A Jarvis spokesman said: "We are fulfilling our school contracts."