Sen. Russell B. Long (D-La.), one of the most influential members of the Senate, announced yesterday that he would vote against the SALT II pact, declaring that it cannot be verified and that Soviet combat troops in Cuba demonstrated Soviet bad faith.

Through Long had spoken critically of SALT II in the past, the Carter administration had hoped for his vote, and most of its optimistic projections for Senate approval of the arms treaty assumed Long's eventual support.

Without Long, administration officials acknowledged last night, the task of finding 67 senators to support SALT will be vastly more difficult. Long is presumed to carry substantial influence with a key bloc of moderate southern Democrats who remain undecided on SALT.

The fact that Long cited the presence of Soviet combat troops in Cuba as a reason for his decision on SALT was particularly painful for the Carter administration, which is both divided and dispirited by the flap set off by recent intelligence findings that a combat-capable Soviet brigade is in Cuba.

Until this was revealed late last month, White House strategists thought their campaign for SALT II was going well. They felt that political momentum was building behind the treaty, and that moderate figures like Russell Long were likely to come down in favor of it.

"If there is one guy who can put his finger up in the wind and say how its blowing, Russell Long is him," one administration official said last night. This source said it was especially significant that Long would exploit the flap over troops in Cuba to announce opposition to SALT II.

Long revealed his decision in an interview with columnist Carl Rowan on WDVM-TV in Washington. "If I had any doubts about it [SALT II], and I didn't have much," Long told Rowan, "my doubts were removed by the last indication down there in Cuba that the Russians are not keeping their faith on the agreement they made with President Kennedy."

Long said that at the end of the Cuban missile crisis in 1962, the Soviets agreed to remove their missiles from Cuba and not to station offensive weapons there in the future. "I don't think the agreement contemplated that they were going to have [combat] troops in Cuba," Long said.

The Louisiana Democrat, who is chairman of the Finance Committee, also criticized the treaty. "I think we could get a better agreement," he said. "And it appears to me this agreement is not going to prevent an arms race. It's simply going to be part of an arms race."

"I don't believe the thing is verifiable."

Long's decision to oppose SALT means, as one administration official put it last night, that "we [the administration] can't afford to lose too many more Democrats," and have any hope of winning the necessary two-thirds Senate approval for the treaty.

White House hopes for moderate southern support for the treaty now must ride on Sen. Sam Nunn (D-Ga.), who has been pressing the Carter administration to increase defense spending significantly if it wants his vote for the arms pact.

Nunn is one of a group of senators meeting early this morning with President Carter to urge him to spend more for defense. Thus far, Nunn has expressed dissatisfaction with the administration's plans for an expanded defense budget.

Another southerner, Richard Stone (D-Fla.), harshly criticized SALT II in a Foreign Relations Committee hearing yesterday. The administration how considers Stone a likely "no" vote.

Both Long and Stone voted for the Panama Canal treaties last year and both are running for reelection in 1980.

Administration lobbyists reckon that without those two, they must get the votes of Lawtan Chiles (D-Fla.), plus both Alabama senators (Howell Hefflin and Donald Stewart, both Democrats), Nunn and Herman Talmadge (D-Ga.), and Robert Morgan (D-N.C.). Chiles and Morgan may be inclined to back the treaty, and the others remain undecided and skeptical.

Virtually all the swing senators have continued to say they are formally undecided on the treaty.