By the time President Barack Obama acknowledged on Monday that his signature health care program had serious problems, it was clear the political stakes had escalated for the White House.

And so that evening Obama gathered some of the top political advisers from his first term for a strategy session on a range of topics. The president himself spent little time on how to handle the political fallout, arguing that fixing the problems of HealthCare.gov, the website at the heart of the troubles, would take care of that challenge.

Not everyone agreed it was so simple.