According to five separate sources with knowledge of negotiations -- including both Republicans and Democrats -- the president offered an increase in the eligibility age for Medicare, from 65 to 67, in exchange for Republican movement on increasing tax revenues.

The GOP proposal itself revives a host of ideas from failed talks with Obama in the summer of 2011. Then, Obama was willing to discuss politically risky ideas such as raising the eligibility age for Medicare, implementing a new inflation adjustment for Social Security cost-of-living adjustments and requiring wealthier Medicare recipients to pay more for their benefits.