CORPUS CHRISTI, TEX., JUNE 28 -- As delegates to the national convention of the League of United Latin American Citizens (LULAC) were gathering here last week, Rep. Richard A. Gephardt (D-Mo.) made a last-minute change in his schedule to speak to a preconvention breakfast meeting of Hispanic leaders.

Sen. Joseph R. Biden Jr. (D-Del.) said he would consider a Hispanic as his vice-presidential running mate as well as for the Cabinet and Supreme Court vacancies.

When Massachusetts Gov. Michael S. Dukakis was asked if he would name a Hispanic to the Cabinet, he replied in Spanish.

"Sin duda -- Without a doubt," he said.

One by one, beginning with Gephardt's hastily arranged appearance Tuesday through speeches by Jesse L. Jackson and Sen. Paul Simon (D-Ill.) today, the seven announced Democratic presidential candidates courted the Hispanic vote with Latin fervor during the four-day convention.

The size of that vote is growing and it could be critical in two Democratic primaries -- in Texas, one of the main prizes in the "Super Tuesday" cluster of contests throughout the South next March 18, and California, where the primary process ends next June.

"We are the fastest-growing group in voter registration and population in the United States and I think that's dynamite," said William C. Velasquez, president of the Southwest Voter Registration-Education Project.

San Antonio Mayor Henry G. Cisneros, who was clearly the most popular politician among all those who visited this coastal city during the convention, urged his fellow Hispanics to begin flexing political muscles more aggressively.

Cisneros called for a meeting of Hispanic leaders from throughout the country to draft a statement of demands to the presidential contenders, including appointment of "at least one and preferably two Hispanics in the Cabinet of the next president."

"It is not enough for the candidates to come here and say what they would do," he said. "It is important for LULAC to say that this is what we must have."

The candidates, who included one Republican, Rep. Jack Kemp (R-N.Y.), did their best to anticipate those demands. Dukakis and former Arizona governor Bruce Babbitt gave portions of their speeches in Spanish, and Babbitt did not wait to be asked about presidential appointments.

"My Cabinet will include Hispanics," he declared.

All the candidates promised a major commitment to education (a top priority in the Hispanic community, where the school dropout rate exceeds 50 percent), to job-creation through economic growth and to bilingual education programs. All but Kemp and Sen. Albert Gore Jr. (D-Tenn.) criticized Reagan administration policy in Central America.

In the most enthusiastically received speech at the convention, Jackson called today for a Hispanic to be appointed to replace retiring Supreme Court Justice Lewis F. Powell.

According to officials of LULAC, the largest Hispanic organization in the country, an informal canvass yesterday of the more than 5,000 convention-goers suggested that Babbitt, who has strong ties to the Hispanic community from his two terms as governor of Arizona, had the most support along with Dukakis, followed by Jackson.

In an equally unscientific straw poll today, Babbitt and Dukakis again led the field with 24 percent each. They were followed by Jackson with 17 percent, Simon with 12 percent and Biden, Gephardt and Gore with 4 percent each.

There was, however, no clear consensus among the delegates. Although Velasquez said Hispanics tend to vote in a bloc and are heavily influenced by endorsements from community and political leaders, there are distinct differences within the Hispanic population. Cuban Americans, concentrated in Florida, generally vote Republican and support President Reagan's policy in Central America, while Mexican Americans, who dominated the LULAC convention, cheered the Democratic candidates as they pledged an end to aid for the Nicaraguan contras.

Cisneros' call for "a unified Hispanic agenda" is "next to impossible," said Jose Botello, a delegate from Dallas.

Cisneros acknowledged that any statement of Hispanic demands "by necessity would have to be a consensus document." But he said agreement on some items, including Hispanic Cabinet appointments, a major federal investment in education and trade and employment policies, is possible.

Regardless of whether such a document ever emerges, the appearance of all seven Democratic hopefuls here underscored the growing importance of the Hispanic vote in Democratic politics. While Velasquez estimated that Hispanics will make up about 4 percent of the 1988 general election turnout, their concentration in Texas and California, which together account for more than one-fourth of the electoral votes needed to win, could make a critical difference in a close election.

According to Robert R. Brischetto, executive director of the Southwest Voter Research Institute in San Antonio, Hispanics account for about 20 percent of the voting-age population in California and more than 22 percent in Texas. Nationally between 1980 and last year, Hispanic voting-age population grew 29 percent, more than four times the growth rate for the general voting-age population, he said.

Most California and Texas Hispanics are Mexican Americans, and in 1984 Mexican Americans in Texas voted 3 to 1 for Democratic nominee Walter F. Mondale, Brischetto said.

None of this was lost on the Democratic contenders, and helped to explain why Kemp was the only Republican hopeful to address the convention. LULAC officials reveled in their ability to attract the entire Democratic field. Several recalled earlier years, when the organization gained scant attention from national politicians of either party.

"At least we're getting attention; we're being courted, and frankly that's a good feeling," said Paul Garza Jr., a former LULAC president from Laredo, Tex. With the Democratic nominating race "wide open," as Cisneros noted, LULAC and other Hispanic organizations can count on being the object of continuing attention in the months ahead.

"There's an old Mexican saying," Garza said, "that when the waters are murky, it benefits the fisherman."