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And they’re facing severe long-term structural problems in the budget and entitlement programs that will begin to inflict real consequences during Mr. Obama’s presidency.

One of Mr. Summers’ signature issues, meanwhile, is income inequality — also a passion of Mr. Obama.

The U.S. ranks 95th out of 135 countries measured in the Gini coefficient, an index of income equalities by nation, as recorded in the CIA World Factbook.

“As a thought leader, Larry has urged us to confront the problems of income inequality and the middle class squeeze, consistently arguing that the key to a strong economy is a strong and growing middle class,” Mr. Obama said.

“This idea is the core of my own economic philosophy and will be the foundation for all of my economic policies,” he said.

And as for Mr. Summers’ reputation as a social misanthrope, his defenders say that is a result of his passion and embrace of honest debate.

“He’s very used to arguing things on the merits,” Ms. Sandberg said.

“Obviously there were issues at Harvard. I don’t think they’re reflective of who Larry is,” she said.

Mr. Summers explained it himself this way.

“I’m somebody who wants their errors to be of trying to do too much rather than trying to do too little, trying to make as large and as constructive a difference as I can. That’s a perspective that I bring to whatever I try to do.”