WASHINGTON—Kent Conrad vaulted from North Dakota tax commissioner to the U.S. Senate in 1986 on the strength of a startling pledge: He would quit and go home if the federal deficit wasn't "brought under control" during his first six-year term.

The deficit that year hit a record $221 billion. Six years later it topped $290 billion. This year, it's expected to hit $1.6 trillion.

Mr....