“Redistribution is a loaded word that conjures up all sorts of unfairness in people’s minds,” said William M. Daley, who was Mr. Obama’s chief of staff at the time. Republicans wield it “as a hammer” against Democrats, he said, adding, “It’s a word that, in the political world, you just don’t use.”

These days the word is particularly toxic at the White House, where it has been hidden away to make the Affordable Care Act more palatable to the public and less a target for Republicans, who have long accused Democrats of seeking “socialized medicine.” But the redistribution of wealth has always been a central feature of the law and lies at the heart of the insurance market disruptions driving political attacks this fall.

“Americans want a fair and fixed insurance market,” said Jonathan Gruber, a health economist at the Massachusetts Institute of Technology who advised Mr. Obama’s team as it designed the law. “You cannot have that without some redistribution away from a small number of people.”