A group of foreign central bankers visiting Washington warned Mr. Bush that he needed to strike a deal with the Democrats who controlled both houses of Congress. Without one, an earlier budget-reduction law was about to trigger automatic cuts even deeper than the so-called sequester looming now.

But the Republican president, long before Grover Norquist became famous, was hamstrung by his own unequivocal no-new-taxes pledge. Once Mr. Bush abandoned it — embracing higher revenues, though not higher rates, just as Mr. Boehner has — negotiations quickened.

Yet at the time the pace felt glacial. After talks in a Senate office building failed, participants moved to Andrews to escape the media spotlight.

Eventually, a smaller group of just eight negotiators, meeting in Speaker Thomas S. Foley’s office, produced a $500 billion deficit reduction package that included $134 billion in taxes and substantial cuts in Medicare. Then Republican conservatives, led by Representative Newt Gingrich, joined liberal Democrats in blowing it up.

After a six-month slog, the White House, offering fewer spending cuts and more tax increases, won over enough Democrats to enact it. “The final agreement was reached largely out of exhaustion and convenience,” former Senator Pete V. Domenici, Republican of New Mexico, said at a recent panel discussion.

The main difference this time? The House speaker, John Boehner, is the odd man out, and he’ll have to get his members to bend the same way Bush did. (Also worth noting: The deal was a success, helping cut back on the debt built up in the 1980s.)