Mexico's 73 million people make it the world's largest Spanish-speaking nation. It shares a 2,000-mile border with the United States. And, as it is struggling to stave off bankruptcy, there is increasing debate here about whether Mexico might bring revolutionary violence besetting Central America to the U.S. doorstep.

Fanning the debate has been the administration's tendency to argue its case for U.S. involvement in El Salvador in terms that recall the southeast Asia "domino theory" of the Vietnam war era.

President Reagan, in his speech March 10 asking for increased military aid to El Salvador, called that tiny nation "the first target" of a Soviet and Cuban campaign to spread communist "revolution without frontiers" through Central America to the U.S. border.

In a television interview last month, Sen. Henry M. Jackson (D-Wash.) said that "the ultimate primary target of communist activity in Central America is the destabilization of Mexico . . . . If a Castro-type government should come to power in Mexico, the demand on the part of the American people to bring our troops home from Europe would be overwhelming, and they would insist that we defend America first."

Despite occasionally overheated rhetoric, there is no evidence to suggest that U.S. officials foresee a situation that would permit Castroite guerrillas to return the U.S. border with Mexico to the days when marauders such as Pancho Villa struck from across the Rio Grande.

In fact, although administration policy-makers are very careful not to say so publicly, many are known to feel that the most immediate effects of Mexico's need to grapple with financial problems are likely to mean far greater cooperation with the United States.

Specifically, Mexico, because of its desperate need to generate more earnings, is expected to increase its role as the biggest source of U.S. oil imports under terms more favorable to the United States.

In Central America, where Mexico's support for leftist movements has caused frequent friction with Washington, its new president, Miguel de la Madrid Hurtado, could limit his government to rhetoric rather than actual attempts to influence events substantially.

U.S. officials dealing with Latin America are keenly aware that the financial crisis into which Mexico was thrown by collapse of the world oil market could have far-reaching implications for U.S. interests in areas as diverse as trade, immigration and narcotics control.

They are aware, too, that the crisis could take on political overtones if de la Madrid cannot navigate successfully between fiscal austerity demanded by foreign creditors and his countrymen's economic and social aspirations. Such a failure could undermine the de facto one-party rule that has kept Mexico politically stable for almost 50 years and push it toward extremes that worry domino-theory advocates.

Secretary of State George P. Shultz, who last August teamed with Treasury Secretary Donald T. Regan to work out an emergency loan of nearly $3 billion to stave off default of Mexico's debts, noted recently that Mexico's problems are financial rather than political, and said, "I believe they can be handled with good work."

Shultz and Regan are to travel to Mexico City Sunday for two days of meetings. The main emphasis will be on mapping a campaign to deal with the debt problem, but U.S. officials have said privately that the entire range of relations will be covered. They expect that the meetings will set the tone of the relationship while Reagan is in office.

Even those U.S. officials who place little credence in the worst-case domino-theory scenarios agree that the United States has a strong vested interest in helping Mexico out of its financial predicament. U.S. banks hold the largest part of Mexico's $80 billion foreign debt, and a default would have seismic effects on the U.S. banking structure.

Mexico also is the third-largest customer for U.S. exports. Its purchases of U.S. goods fell from $18 billion in 1981 to $11.8 billion during 1982, throwing U.S. border merchants dependent on Mexican customers into virtual depression.

A large increase in Mexico's chronic unemployment raises the threat of even greater illegal immigration as the Reagan administration presses for legislation to restrict entry of illegal aliens, which increased 20 percent between October and February.

While U.S. interests point toward greater cooperation and help for de la Madrid, there is implicit a strong suggestion that Washington is not unhappy that Mexico will be increasingly dependent on U.S. financial backing and good will.

Administration officials, diplomatically aware of Mexican sensitivities, strongly deny that they plan to use such dependence as leverage to reassert U.S. dominance. However, there seems to be a sense within the administration that Mexico's troubles will make it more difficult for de la Madrid to emulate predecessors Luis Echeverria and Jose Lopez Portillo in pursuing policies that Washington frequently regarded as nose-thumbing defiance.

Friction began in the 1970s, when discovery of enormous oil reserves triggered a feeling among Mexicans that, after a long history of relative poverty, they would be able to carry out rapid internal development and make Mexico a major force in world affairs.

That led to a boom in public spending and expansion of private industry, built mostly on foreign loans from banks eager to advance large sums on the expectation of steadily climbing oil revenues. Mexico's external debt soared from about $3 billion in 1970 to its present $80 billion.

This overextended position, aggravated by high inflation and an imbalance that saw imports rise at a far faster rate than exports, sent Mexico to the edge of bankruptcy when last year's oil glut and falling prices reduced Mexico's basic earning power.

The oil boom also had a major impact on the foreign policy of a nation controlled for decades by the Institutional Revolutionary Party. Until the 1970s, its most powerful leaders were noted for using radical-sounding, ultranationalistic language to mask basic conservatism that included generally close cooperation with the United States on most issues.

But Echeverria, then Lopez Portillo, apparently believing that oil wealth would make Mexico a major influence within Latin America and the nonaligned movement, turned increasingly to Third World-oriented policies that, in some cases, were viewed here as gratuitous exercises in Yankee-baiting.

Under Lopez Portillo, the United States became the biggest customer for Mexican oil, currently obtaining 685,000 barrels a day or about 14 percent of its crude imports. That is 49 percent of all oil exported by Mexico.

Even establishment of this highly important energy supply relationship was accompanied by bitter haggling over prices and the tendency of the Lopez Portillo government to flirt with the idea that oil could be used to force the United States into major concessions on immigration and greater access to the U.S. market for Mexican agricultural products.

Greatest tension arose in Central American affairs as the result of several factors: Lopez Portillo's desire to become the most influential leader of the region, the need to placate leftist elements of his party by striking militant postures in foreign policy and most important, the Mexican conviction that the way to handle Central American leftists is to co-opt them through friendship and aid rather than by following the Reagan administration's militant approach.

Shultz' predecessor, Alexander M. Haig Jr., used to sum up Washington's exasperation with Lopez Portillo by remarking in private conversation: "The Mexicans are feeding the alligators."

That was a reference to Mexico's efforts to act as advocate and protector of the radical Sandinista regime in Nicaragua, its provision of a base for activities of exiled Salvadoran politicians allied to guerrillas in their country, its advocacy of negotiations between the Salvadoran government and insurgents along lines that the United States says it believes would give a share of power to communist elements and its ostentatious displays of friendship for Cuban President Fidel Castro.

A year ago, the United States bailed out of a Mexican-proposed initiative to seek a U.S. dialogue with Cuba and Nicaragua because the administration had become convinced that the Mexicans were so tilted in their sympathies that they could not be trusted to act impartially.

U.S. officials generally agree that the practical exigencies of Mexican politics will not allow de la Madrid to depart very publicly from his predecessor's policies. But, as one senior U.S. official said, "There can be a difference between what you say and what you actually do.

"Even under Lopez Portillo, the Mexicans demonstrated that they could be very helpful to us on issues like Reagan's Caribbean Basin Initiative, and we now are hopeful that, in a quiet way, they will be willing to play a more balanced and constructive role in looking for approaches to Central America on which we both can agree."