Cuban political and military overtures to the Caribbean's newest government has provoked a strong U.S. diplomatic response that many here believe may succeed only in pushing Grenada farther to the left.

In the six weeks since leftist opposition leaders overthrew its widely unpopular government, this small volcanic island has become the site of a struggle for influence that the United States appears to be losing.

The reason, according to Grenada's new Prime Minister Maurice Bishop, is that countries like Cuba have "helped us to deliver the goods" of a so far successful popular revolution by quickly sending diplomats, aid and arms in response to calls for help directed to the world at large.

The United States, on the other hand, has mainly expressed "concern" and "displeasure" over close Cuba-Grenada ties, and regret that the U.S. budget this year does not contain funds for bilateral assistance to Grenada.

As a result, public opinion here, even among those who profess to be nervous themselves over Cuban influence, has decided overwhelmingly that the United States is a bully, and a stingy one to boot.

A number of the approximately 300-strong community of U.S. citizens living here agree. In letters to the island newspaper, as well as directly to President Carter and other U.S. officials, they have accused U.S. diplomats here of a "lack of sensitivity to the situation in Grenada, a lack of understanding of what [is] really going on, plus [a] patronizing attitude."

The unlikely scene of the big-power regional struggle is an isolated 133-square-mile patch of hills and jungle off the coast of Venezuela where approximately 100,000 people eke out a living from tourism and exports of bananas, nutmeg and cocoa.

For years, Grenada endured the erratic rule of Sir Eric Gairy, who had long run the country as a British colony and then became prime minister on independence in 1974, with little notice from the rest of the world.

While Gairy had been a Caribbean embarrassment known primarily for giving United Nations speeches on behalf of flying saucers, squandering the national funds and repressing his political opponents, few other countries had ever taken either him or Grenada seriously enough to express any particular concern.

Gairy was away on one of his United Nations visits on March 13 when Bishop, a 34-year-old British trained attorney, and other members of the opposition New Jewel Movement quickly and efficiently arrested most of his government and troops and proclaimed themselves the new revolutionary government.

The coup sent shock waves through the rest of the English-speaking Caribbean, a fiercely democratic region that had never before experienced a violent change in government, but most Grenadians seemed overjoyed.

The new leaders quickly soothed regional fears by calling for early elections and announcing their respect for human rights and private property. They politely expressed "deep regret" for two deaths during the brief takeover fighting, and invited the local and international press to visit their approximately 80 prisoners on a tour conducted by Bishop's wife.

Pleas went out to the rest of the world for recognition and financial help in straightening out the havoc wreaked by 16 years of what is known here as "Gairyism." Most of all, the new government asked for help in preventing a countercoup by Gairy, who was stranded in the United States and had issued his own call for arms and mercenaries.

While the United States, Britain and a number of Caribbean nations formally recognized the government within a week, the coup had apparently caught the State Department by surprise. Its files on the new leaders, many of whom studied in Britain or the United States, noted primarily that many of them had visited Cuba and were leftists.

U.S. concern grew on April 6 when a Cuban airliner with "technical difficulties" made an unexpected landing in Grenada and left some passengers on the ground.

With this apparently in mind, the State Department instructed U.S. Ambassador Frank Ortiz, who resides in Barbados, to meet with Bishop.

Nine of the 10 points in Ortiz' instructions concerned reassurances that the United States was keeping an eye on Gairy.

The last point dealt with Grenada's concern over rumors, which some U.S. officials have called "paranoid," that Gairy was organizing a mercenary led countercoup, and noted the United States "also believes it would not be in Grenada's best interest to seek assistance from a country such as Cuba to forestall such an attack."

"We would view with displeasure," Ortiz read from his instructions, "any tendency on the part of Grenada to develop closer ties with Cuba."

Ortiz noted that, while the U.S. aid budget has no provision for bilateral assistance to Grenada this year, he could make available several $5,000 grants for selected projects from embassy discretionary funds.

That night, Bishop angrily went on the radio to tell the country what had transpired, and many seemed to agree with his assessment that the United States had little interest in their fears of Gairy, was trying to pick their friends for them, and wasn't going to substantially ease their desperate economic situation.

The U.S. ambassador had pointedly advised him, Bishop said, that if Grenada continued to speak of "mercenary invasion by phantom armies," the island would lose all tis tourists, many of whom come from the United States. The next day, Cuba and Grenada established diplomatic relations, something that had been postponed, sources said, to avoid upsetting the hemisphere.

Within hours, a Cuban ship had pulled into St. George's harbor and begun unloading crates that the U.S. government believes were arms and ammunition. While making no announcement, the Grenadian government said nothing to dispel that belief, which many Grenadians share.

So far, the ragtag volunteer troops of the People's Revolutionary Army, which seems to have asuaged somewhat Grenada's 50 percent unemployment problem, have been seen only with the British weapons raided from Gairy's arsenal. National Security Secretary Hudson Austin said that Guyana has sent four military training advisers here, but insisted that "Cuba has sent only diplomats.

Last week, for the first time in memory, Grenada's newspaper, The Torchlight, printed an anti-American cartoon. The subject was economic rather than political, showing a begging Grenada asking for "meaningful help" while a rifle-toting Uncle Sam tossed a bill and warned "don't you dare ask me or anyone else for more."