Fifteen senators -- 14 Democrats and one Republican -- gathered in the office of Sen. Edward M. Kennedy (D-Mass.) on Tuesday to plot strategy for history's first televised filibuster. It will be a last-chance effort to kill contra aid.

The idea of stopping President Reagan's plan for $100 million in military support for the contras came from freshman Sen. John F. Kerry (D-Mass.). The senator has been collecting accounts of contra drug-smuggling and gunrunning for months. At a closed meeting where he failed to persuade the Senate Foreign Relations Committee to investigate the charges, Kerry declared he would filibuster against more funds until the $27 million already appropriated is accounted for.

The Senate is not accustomed to following the lead of its juniors in these matters, and some senators shrink from the exercise on the grounds that it could be dismissed as a grandstand effort by a handful of dissidents. On the other hand, they have put aside their usual preoccupation with ego and protocol to show the country that they agree with polls indicating 2-to-1 public opposition to contra aid.

The fear of fiasco has ebbed. The unexpectedly large turnout was reassuring. Said Sen. Carl Levin (D-Mich.), "I have been at very few meetings which have had that many senators." Also, it appears that this filibuster will be the most organized in the annals. Even at this early stage of the planning, several senators have chosen subjects about which they will talk at length. With a television audience tuned in on a review of the whole record, Republicans may be hard put to explain votes for the aid or for cloture to choke off the filibuster.

A number of peace and church groups have already met to mobilize around the key cloture vote. The president will need 60 votes to choke off the filibuster. They will put out the word that no matter what the alibi, a vote for cloture is a vote for contra aid.

Senators did not expect to have to take up the burden of opposing a popular president on an issue that has the force of obsession with him. Said one Democrat, "The House was always much more against the contras than we were." The House, weary of the long siege from the White House, fell on June 25.

Sen. Lowell P. Weicker Jr. (R-Conn.), the sole Republican conspirator, however, spoke for the Democrats when he strode into the room and said hardily, "I am here to tell you this has to be done."

The Democrats were bemused to see that Weicker's fellow Connecticut senator, Christopher J. Dodd (D), was lukewarm. Dodd, an adamant and conspicuous critic of contra policy, wondered aloud whether the politics of the situation did not indicate a different course -- perhaps three days of intense discussion, to be followed by an up-or-down vote, which the president would probably win.

Dodd argued -- he interrupted himself laughingly, because Weicker is sponsor of Dodd's opponent in his reelection fight -- that he was sure the president would go to the country in November elections accusing the Democrats of thwarting him on a vote on the contras and confounding his foreign policy.

Kennedy chose human-rights violations as his subject.

Sen. Gary Hart (D-Colo.), usually a lone operator, has joined the team. He has staked out the ruinously isolating effect of military action on our relations with Central American allies.

Sen. Patrick J. Leahy (D-Vt.) will discuss the folly of putting the CIA back in charge of military operations in Nicaragua. Sen. Paul Simon (D-Ill.) will discourse on the international legal aspects, with attention to the World Court condemnation of CIA-sponsored mining of Nicaragua's harbors.

Levin is considering a review of the Contadora process with emphasis on State Department envoy Philip Habib, who, to the consternation of the White House, came within an ace of bringing about an accord with the Sandinistas.

Sen. John Melcher (D-Mont.) is raring to go. He never liked the contra policy any way, but is now incensed over administration plans to finance it by diverting $300 million in funds for Food for Peace and African famine relief -- "4 million African children die every year." He plans to speak about the deleterious effects of contra aid expenditures on farm exports.

Senate Majority Leader Robert J. Dole (R-Kan.), speaking to the American Security Council Foundation, said he had heard "some talk about a filibuster." He added, "I don't think that would be a very good idea."

The Democrats, however, think it is the best idea they have had in a long time, a last chance to avert another Vietnam, a good chance to show they are not scared to death of Reagan.