The companies that applied to partner with the government to take on banks' bad assets may face restrictions on executive compensation and other elements of their business, the chairwoman of the bailouts' oversight panel said Monday.

"I think these are entirely appropriate questions," Troubled Asset Relief Program (TARP) Oversight Panel Chairwoman Elizabeth WarrenElizabeth Ann WarrenUnited Auto Workers strike against GM poised to head into eighth day Omar: Biden not the candidate to 'tackle a lot of the systematic challenges that we have' Seven takeaways from a busy Democratic presidential campaign weekend in Iowa MORE asserted during an appearance on CNBC.

"If you want to take taxpayer dollars, you cannot conduct business as usual," Warren argued. "You are now involved in a giant government program in which we are spending taxpayer dollars to try to support a market that is clearly stumbling."

While companies that have directly received bailout funds have been subject to regulations on their compensation and spending, Warren indicated those practices could very well spread to the 100 investment firms that have applied to the Treasury Department to the Public-Private Investment Program (PPIP).

The names companies who are accepted into the program, in which private firms would take on financial institutions' toxic assets with government backing, could come as early as the end of this week.

The caps on executive pay have been a hot-button issue politically, perhaps reaching its apex when the American Insurance Group (AIG) having awarded bonuses to its employees while on the taxpayer dole. Congress attempted to recoup those bonuses after the AIG news sparked public outrage.