Ms. Tavenner said that Ms. Snyder was prepared to step down at the end of 2012, but stayed on the job “at my request to help me with the challenges facing C.M.S. in 2013.”

Her official biography says that Ms. Snyder was responsible for “standing up new programs and activities required by the Affordable Care Act.”

The agency provides health insurance to more than 100 million people and spends more than $800 billion a year, which is substantially more than the Defense Department budget.

A former agency official who had predicted Ms. Snyder’s departure said Monday: “She had to go. She was responsible for the implementation of Obamacare. She controlled all the resources to get it done. She was in charge of information technology. She controlled personnel and budget.”