Next week, six of the Democratic presidential candidates will be vying for what is widely considered the singlemost coveted union endorsement, that of the Service Employees International Union, which represents 1.9 million workers.

On Monday, those Democratic candidates will be speaking at the S.E.I.U.’s political action conference at the Washington Hilton, where 1,500 of the union’s leaders and activists will gather. On Wednesday, Sept. 19, the union’s board will decide whether to endorse anyone at that time. The S.E.I.U. is the nation’s second largest union, behind the National Education Association, which has 3.2 million members, but political experts agree that the S.E.I.U. is the more potent force.

Union officials say former Senator John Edwards has mounted a full-court press to persuade the S.E.I.U.’s top officials to endorse him, but Hillary Clinton’s camp and Barack Obama’s camp are maneuvering vigorously to try to deny Mr. Edwards the organization’s backing.

Union officials say that some top S.E.I.U. officials are leaning toward Mr. Edwards, attracted by his strong support of universal health insurance and his vigorous support of unionization drives. But the S.E.I.U.’s leaders are concerned not only that the union’s rank-and-file is not nearly as supportive as Mr. Edwards as they are, but that Mr. Edwards continues to lag well behind Mrs. Clinton and Mr. Obama in nationwide polls.

Two steps are required for the S.E.I.U.’s 60-person board to endorse a candidate. First, board members representing 50 percent of the union locals that have members on the board have to agree that the union should make an endorsement. Second, board members representing 60 percent of all the union’s overall membership have to agree on whom to endorse.

One union official said that the S.E.I.U.’s leaders in California are strongly in favor of Mr. Edwards, but that many S.E.I.U. leaders in Illinois and New York are enthusiastic about Mr. Obama and Mrs. Clinton and oppose a unionwide endorsement of Mr. Edwards.

Union officials say it is very unclear whether any candidate will be able to surmount the 60-percent threshold. It may come down to whether Mr. Edwards — or another candidate — gives a speech next Monday that sweeps the S.E.I.U.’s leaders and political activists off their feet.

The Democrats taking part are Senator Joe Biden of Delaware, Senator Chris Dodd of Connecticut, Mr. Obama of Illinois, New Mexico Gov. Bill Richardson, Senator Clinton and Mr. Edwards.