UPDATE 1-W. House mulls unwinding 'too big to fail' firms

WASHINGTON Oct 26 (Reuters) - A council that includes the U.S. Treasury Secretary would help set policy for dealing with troubled financial firms under White House plans to deal with the "too big to fail" problem, CNBC television said on Monday citing sources.

The Obama administration would give the Federal Deposit Insurance Corp authority to unwind large firms whose failure could threaten the overall economy.

Federal regulators say such "resolution authority" is crucial to ensuring that the market does not think that some firms will always be rescued by the government.

The U.S. government was forced to improvise last year in crises at big financial firms such as investment banks Lehman Brothers and Bear Stearns, as well as insurer AIG (AIG.N). (Reporting by Rachelle Younglai; Editing by James Dalgleish)