THE joke in Washington is that Hillary Clinton does not want to be vice-president because she already did the job when Bill was in the White House. The question is: who will want to play third banana to her husband in Hillary’s administration?

Until Dick Cheney, the current vice-president, came along the office was considered unmanly. President Harry Truman said history regarded it as “about as useful as a cow’s fifth teat”. Yet Al Gore, Bill Clinton’s vice-president, nearly succeeded him at the White House and went on to win last year’s Nobel peace prize for his work on climate change.

Morris Reid, a fundraiser for Clinton, believes the Goracle, as Gore is known, should bang heads together and persuade Obama to team up with Clinton as her “veep”.

“This is the first time the Democrats have a ticket that could lock up the White House for the next 16 years,” Reid said. “It’s very clear that they are stronger together than apart.”

A race like a crackpot Dynasty

The contest between Barack Obama and Hillary Clinton matches any fiction

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Terry McAuliffe, Clinton’s campaign manager, floated the idea for the first time last week, raising hackles among the Obama camp that he was plotting to undermine their candidate’s vote on the eve of Super Tuesday by misleading voters into thinking they could have them both.

Until recently a Clinton-Obama pairing had been ruled out on the grounds that there would be too much “making history” with the first woman and the first African-American candidate, and the personal chemistry between them remains frosty. It is not a “dream ticket”, said Donna Brazile, Gore’s former campaign director: “It’s a fantasy ticket.”

For Clinton, Obama and John McCain, the soon-to-be-crowned Republican nominee, there is a strong case for appointing a governor with executive experience to balance their background as senators in Congress’s talking shop.

Mike Huckabee, the last man standing in the Republican race against McCain, is likely to be knifed by McCain once he wins.

Charlie Crist, the governor of Florida, is a more attractive proposition because he could bring votes to the Republicans in a crucial swing state - in the same way that he swung voters behind McCain in last month’s primary.

McCain is also said to be considering Mark Sanford, a social conservative and governor of South Carolina, and Tim Pawlenty, governor of Minnesota, an old friend.

The obvious choice for Clinton is Ted Strickland, the governor of Ohio, a must-win swing state that could deliver the White House to the Democrats this year. Evan Bayh, senator and former governor of the conservative state of Indiana, is another potential pick.

Obama might be tempted by Strickland, even though he has endorsed Clinton, or Tim Kaine, governor of Republican-leaning Virginia. Other possibilities are Kathleen Sebelius, governor of Kansas, where Obama’s mother was born, and Tom Daschle, the former senator for South Dakota and the éminence grise behind Obama’s well-run campaign.

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