The nominee, Bill Clinton, re-wrote his acceptance speech to include an appeal to Perot supporters, and delegates, analysts and party professionals pondered the possibility that Mr Perot's withdrawal could hand back crucial support in November to President George Bush.
In a three-way race, the hope of Democrats had been that a reasonable showing by Mr Perot, particularly in the South and West, could have opened a breach for Mr Clinton to ease in and steal crucial states, such as Texas and California, from the Republicans. Now that political map, which seemed to offer so much opportunity, has been torn up.
The vital task for Governor Clinton last night was not only to unite Democrats behind him, but to persuade the many millions of disappointed Perot volunteers to see in him what they saw in the Texan billionaire: a leader offering genuine change and relief from the perceived gridlock of politics-as-usual in Washington and economic slide.
The scramble to woo Perot backers began minutes after the billionaire's withdrawal announcement in Dallas. The Democratic Party chairman, Ron Brown, swiftly pleaded for their support, urging them to 'join our crusade to put the people first'. He told them: 'Take heart, don't be disappointed. I appeal to you to join Governor Clinton to help change our country.'
Just as quickly, the Republicans issued a similar invitation, saying that they were the 'natural home' for Perot volunteers. Interrupting a fishing trip in Wyoming, Mr Bush called journalists to deliver his own message. 'Now we will make it clear to all the Perot supporters that we share many of their principles and we welcome them warmly into our campaign,' he said.
As well as the volunteers, both parties moved to court Mr Perot himself. Mr Clinton telephoned Mr Perot at his Dallas base, ostensibly to congratulate him on his courage in deciding to quit the race. Clearly, though, any personal endorsement by Mr Perot of the Clinton-Gore campaign could translate into a very significant underpinning of popular support.
Some officials even suggested yesterday that Mr Perot had been invited to fly up to New York to make an appearance at the Democratic convention. Mr Brown denied such a possibility, however.
The more optimistic Democrats consider that Mr Perot has already done his work in helping Mr Clinton towards the White House. Undoubtedly, the steep climb achieved by Mr Clinton in opinion polls over the past three weeks, even before the convention itself, has happened partly because of the warfare between the Republicans and Mr Perot.
It has also been noticeable that much of the recent slide in the popularity of Mr Perot, from the mid-30s to just 20 per cent in the latest poll, has been reflected in the rise of Mr Clinton's ratings, suggesting a shift already of Perot people to the Clinton-Gore ticket.
The latest ABC-Washington Post poll, in the old three-way scenario, showed Mr Clinton at 45 per cent, compared with 28 per cent for Mr Bush and 20 per cent for Mr Perot. No one is allowed to forget, however, the historical symmetry here with the identical 17 per cent lead held by Michael Dukakis at the end of the 1988 Democratic convention, which was reversed into defeat in the election.
Delegates are mindful also that the advantage gained from the Bush-Perot conflict of recent weeks came partly because Republican fire was drawn away from the Democrats. The Republican team, not famous for gentle play, is now free to direct all its guns at Mr Clinton and at his perceived personal vulnerabilities, including his alleged maritial infidelities.
Meanwhile, Republican officials served notice yesterday that they would begin intensive campaign efforts immediately in those Southern states so crucial to both parties, just as Mr Clinton and his running mate, Al Gore, are planning to set off from the convention tomorrow on a week-long bus tour of Eastern and Mid-Western states.