For much of this week, Hillary Clinton has been having dinner each night with her brothers and her mother at the White House. Bill Clinton, who in the past has often missed dinner with family, has been attending several of these family gatherings.

While public speculation has been focused on Mrs Clinton running for the US Senate (speculation acknowledged last night as not without foundation by her spokeswoman, Marsha Berry), a friend of the Clinton's says that the real discussions at dinner have involved another scenario: Mrs Clinton as vice-president, running on a ticket with Al Gore.

The impetus for this discussion has been the likelihood that the Republican ticket in the 2000 election will be George Bush, son of the former President, and Elizabeth Liddy Dole. That would be a formidable team, and would threaten to siphon the so-called "women's vote" away from Mr Gore.

"It is the Liddy thing that really sets her off," said this source, of Mrs Clinton. "Her place on the ticket would stop any erosion of the gender gap."

The matter has been so discussed in such detail that even the matter of what the Democratic ticket would be called has been considered. Rather than Gore-Clinton, which might confuse voters, the ticket would more likely be called Gore-Rodham-Clinton, using Mrs Clinton's maiden name, which she normally uses.

The interaction between Mr and Mrs Clinton at these dinners has been cordial, and it is clearly, said this source, "a relationship that is, whatever else, working." Yesterday, the reaction across America to the Senate's acquittal ranged from strong polarisation to apathy.

"The consensus is, thank God it's over," said Maynard Davus, a Los Angeles lawyer who watched the vote on television with a group of office workers.

"Thank God it's over."