(FORTUNE Magazine) – No patience. Not collegial. Uncomfortable in the background. Reluctant to compromise. No respect for institutional traditions. Proven inability to suffer fools. Incapable of small talk. By any measure, New York Mayor Rudy Giuliani and First Lady Hillary Clinton have the textbook characteristics of lousy Senators. If one of the great mysteries of politics is how some Senators actually get elected, a greater one is why some of them run at all.

Clinton, for instance, could run a foundation, where she would have much more influence over much more discretionary spending. She could be a high-profile college president and elevate the family pastime of fundraising to new levels. She could earn zillions in a Washington law firm, continue to be a political force--and succeed Vernon Jordan as the capital's greatest fixer. But, no, it has to be the Senate, where grown men and women hold each other hostage to win a $250,000 grant to research caffeinated chewing gum in Illinois or $750,000 to study grasshoppers in Alaska. (I did not make those up.)

Why would one of the nation's most accomplished women want to be a Senator when many of the Senate's best and brightest (Sam Nunn, Warren Rudman, David Boren) have given up in frustration? Maybe to build a separate life from her husband's (no spouses on the Senate floor, and certainly no spouses at surface transportation hearings in Schenectady or agricultural forums in Cattaraugus County). Maybe to go where no First Lady has gone before. Maybe to redeem her self-respect after the most humiliating tenure as First Lady in the nation's history.

Here's the most plausible explanation: If you told graduating seniors in the Wellesley class of 1969 that their most outspoken classmate would be sitting in the U.S. Senate 32 years later, asking Ted Kennedy to co-sponsor her bill on women's health, fighting Strom Thurmond to win approval of legislation ensuring equal pay for equal work, battling Bob Byrd over the pork-barrel provisions he hid in an appropriations bill, nobody would have been surprised. In fact, they would now think Clinton was simply getting back on track.

But trading the dignity of the East Wing for the indignities of the Senate? That's going to be a lot harder than it looks. So is being the junior Senator from New York, deferring to Chuck Schumer. Not to mention guarding New York's interests at meetings of the forestry, conservation, and rural-revitalization subcommittee of the Agriculture Committee. (New York is one big farm.) Or figuring out which worthy applicant from Marilla or Cheektowaga ought to be postmaster. Or remembering that Oswego is on Lake Ontario, and Owego is near Pennsylvania. And one thing more, enough to chill the hottest Hillary supporter: If the Republicans retain control of the Senate, which seems almost certain right now, the grief will be all the greater for Senator Hillary Rodham Clinton (D-N.Y.).

DAVID SHRIBMAN is the Washington bureau chief of the Boston Globe and a Pulitzer Prize-winning political reporter.