It certainly sounds like something he'd do. Check out this tidbit buried in an AP story from yesterday:
Each side offered accounts of secret maneuvering designed to put the other side in a poor light.
Democratic officials said Obama called Boehner on Saturday night, one day after the collapse of compromise talks, and offered to reduce his demand for new tax revenue by $400 billion.
In return, Obama said that he wanted Republicans to abandon their demand to cancel parts of the year-old health care law if future deficit cuts did not materialize.
This official said Boehner rejected the proposal on Sunday.
