The two men, who have been friends for years, discussed the fate of the Downing Street declaration and the prospects of Gerry Adams finally being given a visa to enter the United States.
The meeting was to trigger a co-ordinated lobbying of the Clinton administration that culminated in a diplomatic rout for the British Embassy in Washington.
Mr Hume, who is revered by many in the Democratic National Party, has cultivated an extensive network of politicians and business contacts over the past two decades.
He informed Senator Kennedy that providing Mr Adams with the visa he has been denied eight times in the last 20 years could help the declaration.
Senator Kennedy enlisted the aid of other key committee chairmen, like Senator Christopher Dodd and Senator Daniel Moynihan, both powerful politicians with ethnic Irish constituents, to the Adams visa cause. The fact that they are men on whom he depends for his own domestic agenda was not lost on President Clinton.
From the beginning of the Ulster conflict, the Irish-American political establishment has devoted a considerable amount of energy to denying Sinn Fein, or its North American arm, Noraid, a public platform in the US. The rejection by the overwhelming majority of Irish-American politicians of the IRA's violence ensured a hostile reception for the IRA's message and kept the Irish-American community - some 40 million strong and now the wealthiest ethnic group in the US - from being a powerful political force on this issue.
The Hume-Adams dialogue, and subsequent Downing Street declaration has made the Irish nationalist agenda respectable and given the community a new and powerful voice in American politics. Irish-American Catholic voters are a key swing vote in US politics, which was a factor in persuading President Clinton that it would be unwise to rebuff them over the visa - as he had already done twice in the past 12 months.
During his presidential campaign, Mr Clinton told a hastily arranged Irish-American forum that he would, if elected, give Mr Adams a visa, that he would send a peace envoy to Northern Ireland, and that he would take up the cudgels against London (and the IRA) for human rights abuses.
The trade union movement - traditionally an Irish fiefdom in the US - also weighed in on behalf of Mr Adams, with the umbrella AFL-CIO union telling the Clinton administration that the peace process in Northern Ireland was something that many of its members were concerned about.
The president's decision to grant the temporary 48-hour visa came late on Saturday. The decision was almost derailed by bomb hoaxes in San Diego, California, which mystify officials. Three practice grenades were found at the Shakespeare Pub and Grille, a curio shop called All things Bright and British, and at the federal courthouse. A caller said they were to protest at the failure to give Mr Adams a visa.
It was only when Mr Adams renounced the bomb hoaxes that the administration finally relented.