Franklin D. Roosevelt's first Vice President, John Nance Garner, was quoted as saying the vice presidency isn't worth a pitcher of warm spit. But he didn't put it quite that way. "Cactus Jack" actually used the word "piss," and when a reporter changed it to "spit" for the family newspaper he worked for, Garner called him a "pantywaist." Nowadays, the problem with the quote is that it's not true. Nearly half of the presidents since World War II have been veeps first, and the job has become much more powerful. That makes choosing a running mate a more complex challenge than it once was, as Barack Obama is about to find out. He should think of the office not as a bodily fluid but as a curriculum with three subjects: Geography, Chemistry and International Relations. Anyone who can meet at least some of these requirements merits inclusion on the list fancifully floated by what Russell Baker calls "The Great Mentioner."

Geographical balance hasn't proved decisive since LBJ helped JFK carry Texas in 1960. But Obama may feel he needs to secure Ohio to reduce his risk. That makes Gov. Ted Strickland, a former pastor and strong Hillary backer (both big pluses), a possibility, though he'd need more scrutiny. Gov. Ed Rendell of Pennsylvania has said he's not interested, but Gov. Bill Richardson of New Mexico is. Richardson would help with Hispanic voters, where Obama has trouble, but he didn't make the cut in 2000 and 2004, which doesn't bode well for him.

The other geography play is Virginia, which Obama believes he can turn blue. Popular former governor Mark Warner is a successful entrepreneur, which is an asset. But Warner has yet to explain fully why he dropped out of the 2008 presidential race when he was doing well. And he would have to abandon his current campaign for the Senate, where a President Obama would need every Democrat possible to move his agenda.

Sen. Jim Webb would also have to leave his Virginia seat. Webb is a twofer: Geography and national security. Although he only won his 2006 Senate campaign narrowly (and was stiff and stubborn on the stump), Webb, a Vietnam veteran and former Navy secretary under Ronald Reagan, could help inoculate Obama on defense. Every time John McCain tried to make Democrats look soft on terror, Webb could wave his son's Iraq combat boots. His Scots-Irish brawler heritage would score with Appalachian voters who distrust Obama. On the negative side, Webb, a prolific author, wrote a 1979 magazine article entitled "Women Can't Fight" that would harm him with women still sore over Hillary Clinton's treatment.

There's a third veep-ready Virginian: Gov. Tim Kaine. He's a twofer, too (Geography and Chemistry). After Kaine and Obama learned that their grandparents all lived in the same tiny Kansas town, they became friends. Kaine, a Catholic who got elected by a healthy margin in a conservative state despite opposing the death penalty, lacks any foreign-policy experience. But some Obamanians believe that adding a candidate with national-security credentials would look defensive and accentuate McCain's advantage in experience. If that argument carries, it would open the door to other candidates like Montana Gov. Brian Schweitzer (who would have big appeal among independents) and Kansas Gov. Kathleen Sebelius, an Obama friend (more Chemistry) and the daughter of former Ohio governor John Gilligan (more Geography). Sebelius is experienced and compelling on the stump. But bypassing Hillary to pick another woman might be seen as insulting, at least at first, by voters who think Hillary earned it.

If Obama prefers a sober white guy who is credible on International Relations, he'll consider retired Gen. Wesley Clark, a staunch Clinton supporter who has never held office but ran respectably in 2004. So, of course, did Sen. John Kerry, an early Obama backer and national-security expert whose unprecedented selection would make Obama look exceptionally secure. Kerry is still popular in the states he carried, but Democrats are notoriously hostile to losers. His 2004 running mate, John Edwards, says he doesn't want a sequel, but he could help Obama with working-class whites. If Chemistry is key, Obama could pick Tom Daschle, though Daschle couldn't even carry South Dakota for him last week.

Then there's Connecticut Sen. Chris Dodd, who failed to excite voters this year but earned Obama's admiration and respect. Popular Sen. Bob Graham, an early opponent of the Iraq War, has also been a governor and could help shore up Obama in Florida, where he's lagging. Sam Nunn is nearly 70, out of the Senate for 12 years and politically rusty. But the Georgia Democrat might make that state competitive, with the help of 600,000 currently unregistered black voters. He signaled his availability recently by abandoning his support of the military's outdated "don't ask, don't tell" policy on gays. Nunn's signature issue, stopping the spread of nuclear weapons, was also Obama's priority (along with Richard Lugar) in the Senate. Picking Nunn would highlight that issue's centrality and signal a turn to the center.

Hillary doesn't pass Geography or, obviously, Chemistry, and we know that in Obama's eyes, she also flunked delegate math. Her unseemly efforts to jam her way onto the ticket backfired. Her impressive 18 million voters won't desert Obama en masse, though it's still unclear how many will either vote for McCain or stay home. If the Clintons somehow subjected themselves to vetting and she got picked, Obama would then have to worry about his own supporters being disillusioned, and wonder when Hillary and Bill will act out again.

That could be a bigger problem if she's not selected. Consider LBJ's advice that it's better to have rivals inside the tent pissing out than outside the tent pissing in. And speaking of rivals, remember that Obama recently told an audience that Doris Kearns Goodwin's "Team of Rivals," a history of how Abraham Lincoln brought his enemies into his cabinet, might apply to his approach to Hillary. Never say never in politics, though an awful lot of people in Obama's orbit have been saying it lately.