Carpenter, 62, is a former Citigroup Inc senior executive, having headed the global corporate and investment bank and the alternative investments business.
GMAC has taken $12.5 billion of rescue funds from the U.S. government, and the U.S. is looking to give it about another $2 billion to $5 billion.
But in a statement, GMAC said it has asked the U.S. Treasury to postpone any decisions about putting more capital into GMAC until Carpenter and other management have assessed the current situation.
Al de Molina was Bank of America's chief financial officer earlier this decade, and his departure spurred new speculation that he was in line to become CEO of the bank.
De Molina spent nearly two decades at Bank of America in a variety of senior management positions. He became chief financial officer in September 2005, and resigned from the post on December 31, 2006.
The bank can't catch the big fish they're hunting in this search, but if you find someone from the outside, he's got to be on that list now, said Anton Schutz, portfolio manager at Mendon Capital Advisors, which owns 371,000 Bank of America shares.
But de Molina did make some enemies at Bank of America, recruiting away bank employees when he joined GMAC Financial in 2008, which according to the Wall Street Journal, diminishes his chances of being CEO.
GMAC has been clobbered by the deteriorating auto and housing markets. Earlier this year, a government stress test said the company needed to raise about $11.5 billion of new capital.
U.S. Senate Banking Committee Chairman Christopher Dodd said earlier this month that GMAC would get between $2 billion and $5 billion of taxpayer capital beyond what it has already received.
Carpenter joined CIT Group's board during the company's May 2009 annual meeting, and is now resigning from that spot.
(Reporting by Dan Wilchins and Joe Rauch; editing by Carol Bishopric, Bernard Orr)