A secret of his success has been his ability to strike alliances with key Democrats.
Several negotiators, including one key Democrat, said then that, for political reasons, those increases could not be reduced if Social Security was exempted.
Senator Nunn is a key Democrat on arms-control issues.
Along the way, the story goes, he alienated some key Democrats for closing his office door and catering too much to Congressional Republicans.
He is talking tough, they say, mollifying the conservatives, while making private contacts with key Democrats.
In the House, there is little consensus yet among key Democrats, and no bill has yet been formally introduced.
Similarly, senior officials say they are negotiating with key Democrats on the welfare issue in the hope that a bill emerges that "we can sign."
Discussions of the points in the alleged "compromise" only concerned convincing key Democrats not to acquiesce in a filibuster.
The defection of key Democrats in the Senate on the proposed energy tax also added to doubts about the outlook for the the economic program.
"Not necessarily," said a key Democrat, Senator Sullivan, who described the options as limited.