While the United States tries to bring the deluge of Cuban refugees under control in Florida, U.S. officials here and along the border fear the floodgates may have been opened wide to illegal immigrants from Mexico.

Few of these immigration officials believe that the number of Mexicans and Central Americans illegally attempting to cross the border has declined from the estimated 2 million or more a year of the late 1970s. In recent weeks, however, the number of arrests made by the border patrol has dropped as much as 40 percent at several key crossings.

As a result of this decline, officials here say the number of illegal aliens who previously might have been caught entering the United States in the last month easily may equal the number of Cubans who have landed at Key West.

The officials are careful to say there is no way of knowing for certain, since there are no records of immigrants who evade the Border Patrol. "But you talk about 60,000 in Florida," said an immigration official here, "that's nothing compared to the border."

"They're just running over us something terrible," said regional Border Patrol Chief Donald Cameron, whose jurisdiction, San Ysidro, Calif., is across from Tijuana, Mexico. Traditionally it has the highest number of arrests in the country.

The temporary transfer of more than 100 Border Patrol agents from the Mexican border to Florida to help cope with the Cubans is only part of the problem, according to immigration officials.

"If we had all the money and all the people we could use," said Border Patrol Deputy Chief James Selbe in McAllen, Tex., "Then we could afford to lose 10 or 20 percent of the staff."

But the Border Patrol has long suffered from a chronic shortage of personnel. The budget, drawn up in 1978, is crippled by inflation and rising gasoline prices. In several jurisdictions, patrols had to be cut back when there was simply no money to buy fuel for the cars.

In such a situation any extra drain on resources can be disastrous and over the last year, the U.S. Immigration and Naturalization Service, of which the Border Patrol is a part, has been confronted by one unforeseen crisis after another.

The influx of refugees from Indochina, the boat people of Haiti, the investigation of Iranian students and now the more than 70,000 Cubans arriving in the United States in the last month all have taken time and attention away from the border.

According to U.S. immigration officials based here in Mexico, this distraction comes just as pressures on the 2,000-mile frontier are mounting.

Unrest in Central America is adding increasing numbers of Salvadorans, Nicaraguans and Guatemalans to the ranks of those seeking to slip into the United States. Despite its new oil-based affluence, Mexico has not yet been able to resolve its tremendous problems of unemployment and population pressure, the most compelling factors driving its workers to cross the border in search of jobs. According to one immigration official here, "It's only going to get worse."

Added to the practical difficulties are what many immigration officials see as the moral and political ambiguities of their job. Those here in Mexico, for instance, find themselves repeatedly confronted by the question of why Cubans, who in many cases left for economic reasons, have been welcomed to the United States while Mexicans with similar motivations must make often dangerous clandestine border crossings.

Donald Cameron in San Ysidro says he has lost more than 60 officers out of his force of about 500 in the last year, most of them retiring or going to other agencies.

As a result, Cameron said, the number of arrests made in his heavily traveled jurisdiction has dropped from 27,500 during the first three weeks of May 1979 to 19,700 during the same period this year.

Cameron said he requested trained temporary replacements to fill out his staff and believed he was about to get them when he saw them go to Florida.

The agents in Florida primarily have been detailed to patrol and prevent Cuban refugees from avoiding the detailed screening process required for their formal admission.

The agents are being rotated from all parts of the country and some have now returned to their border posts.

Richard P. Staley, Border Patrol chief in El Paso, said that while 50 of this 400 men were on temporary duty in Florida at the beginning of the month, his office caught 30 to 40 percent fewer suspects.