WASHINGTON -- Government officials seeking to revamp the U.S. financial bailout have discussed spending another $1 trillion to $2 trillion to help restore banks to health, according to people familiar with the matter.

President Barack Obama's new administration is wrestling with how to stem the continuing loss of confidence in the financial system, as it divides up the remaining $350 billion from the $700 billion Troubled Asset Relief Program launched last fall. The potential size of rescue efforts being discussed suggests...