President Reagan today assailed the Soviets "and their henchmen in Havana" for spreading "repression and terror" in Central America, and warned that "our biggest obstacle is not foreign threats" but those "soft speakers" in the United States who oppose his Latin policies.

In a speech bristling with attacks on communism that capped a day of campaigning in the Cuban American community here, Reagan unleashed a rhetorical broadside at "the new colonialism" of Cuban dictator Fidel Castro in Central America.

The president directed equal criticism at Marxist influence in Central America and at those in Congress who are resisting his efforts to boost military and economic aid to the El Salvador government and to "freedom fighters" opposing the Sandinista regime in Nicaragua.

Insisting that "the biggest obstacle" to this anti-communist effort is a "lack of confidence and understanding" at home, Reagan said:

"The United States is at a crossroads. We can no longer ignore this hemisphere and simply hope for the best. There are far too many people trying to find excuses to do nothing.

"If we are immobilized by fear or apathy by those who suggest that because our friends are imperfect we should not help them . . . then the American people will know who is responsible and judge them accordingly," Reagan said in a pointed reference to Democrats who have been unwilling to join the administration's thrust against communism in Central America.

Quoting President Theodore Roosevelt's admonition to "speak softly and carry a big stick," Reagan said of his opposition, "Well, there are plenty of soft speakers around, but that's where the similarity ends."

"We will not permit the Soviets and their henchmen in Havana to deprive others of their freedom . . . , and some day Cuba itself will be free," Reagan told a wildly cheering crowd of about 1,500 packed into the Dade County Auditorium to celebrate the 81st anniversary of Cuba's independence from Spain. Hundreds more lined the streets outside, waving Cuban and American flags and carrying banners such as "Hands Off Cuban Freedom Fighters."

Interrupted a dozen times by standing ovations, Reagan said in his speech to the Cuban American National Foundation, an anti-Castro group:

"The Soviet Union, with all its military might, with its massive subsidy of the Cuban economy, can't make the system produce anything but repression and terror."

He added that "our friends" in Central America "cannot be expected to stand unarmed against insurgents who'd been armed to the teeth by the Soviet-Cuban-Nicaraguan axis."

Leaving behind the more restrained discussion of the last few weeks about arms control with the Soviets, Reagan returned to a more strident anti-communist tone in his speech today.

"You know, they say there are only two places where communism works," the president said. "In Heaven, where they don't need it--and in Hell, where they've already got it.

"Don't let anyone fool you, what's happening in Cuba is not a failure of the Cuban people, it's a failure of Fidel Castro and of communism," Reagan said.

The president renewed his charge that there is "strong evidence" that Castro's regime is "peddling drugs like criminals, profiting on the misery of the addicted." He demanded an "accounting" from Castro but stopped short of blaming him directly.

White House spokesman Larry Speakes said Reagan's charge was based on "intelligence information" that won't be disclosed. Last November, four high-ranking Cuban officials were indicted in Miami on federal drug smuggling charges, and allegations of the Castro regime's involvement in the drug trade were recently aired at a hearing in Miami.

Reagan has long been a popular figure among Cuban exiles in Miami. His visit today fired up passions as anti-Castro "freedom fighters" paraded with signs urging another effort to dump the Cuban regime.

The president, however, had another mission in mind: to lay the groundwork for a possible 1984 reelection bid that will depend, in part, on Hispanic support.

In a gesture to the large Latin community here, Reagan announced today that Jose S. Sorzano, a former Georgetown University professor and a native of Cuba, will be nominated to be deputy U.S. ambassador at the United Nations, succeeding Kenneth L. Adelman.

Before his speech today, Reagan lunched on roast chicken, rice, plantains and black beans in Miami's Little Havana section.

At the auditorium there were chants of "1984," but Reagan merely dropped his familiar, noncommittal hints about his reelection intentions. Speakes said the cost of the trip would come out of federal funds because Reagan came to celebrate Cuba's independence day. "Any resemblance to a political event is purely coincidental," Speakes said.