WASHINGTON -- The Treasury Department has committed nearly $10 billion more than the $350 billion Congress has authorized to date for the financial-sector rescue package, which could constrain how the incoming Obama administration deploys the rest of the fund.

Treasury's announcement Monday that it is directing $6 billion to auto-finance company GMAC LLC brought to $358.4 billion the total funds from the Troubled Asset Relief Program that have been pledged to a variety of programs and guarantees. That suggests Treasury is...