Bullfights instead of baseball?

One time Chief Ben American Horse of the Sioux stopped at the Capitol to visit Alben Barkley, who was then vice-president. After a long discussion the chief rose to leave. He paused, looked the vice-president impressively in the eye and observed: ''Young man, let me give you a word of advice. Watch your immigration laws. We were careless with ours.''

I thought of that advice last week as I read the front-page story in the New York Times (March 19) beginning ''The stream of illegal aliens pouring into the United States has become a torrent, driven by the currency crisis that has shattered the Mexican economy.''

A new immigration exclusion law (S 529) is pending in Congress, strongly supported in testimony by Attorney General William French Smith. For the first time it penalizes employers who knowingly hire illegal aliens. There has hardly ever been a greater influx of these. ''At the root of the illegal immigration,'' says Mr. Smith (Feb. 28), ''is the ready access of illegal entrants and visa abusers to jobs that are very attractive when compared to employment opportunities in their homelands.'' Does America have the will to stop them? We should know before long. At the heart of the matter is a paradox. I know of nothing like it in other countries. The US is preparing a military budget of $ 245 billion to defend its borders. But we are assigning only about $77 million for our border patrol.

As it works out, only about 350 US patrolmen are on the job at any one time to defend the Mexican border which is 1,954 miles long. There are approximately 12 million American workers who simultaneously can't find jobs. The Mexicans and other aliens pour in all the same, experience shows; they are better off in the US than in a different kind of ''unemployment'' that currently exists at home.

Let the Times' account tell the story: ''the Border Patrol is inundated''; the number of deportable aliens ''is up almost 50 percent'' from last year; ''perhaps one in three will be apprehended by the thin line of Border Patrol officers, and bused back (to Mexico) but they will try again in a matter of hours.''

Statistics help explain the situation. The US has brought its own population increase under control at about 0.8 percent a year. Mexico hasn't. Its natural increase is about three times ours and is one of the highest in the world. Now the money crisis has increased problems in Mexico; at present in Ciudad Juarez unemployment is around 40 percent.

What happens if the Mexican tide continues? Will parts of the United States become bilingual? Will there be bullfights instead of baseball? There is no racial bias in this analysis; it is a matter of wonder how this quiet but global demographic contest will come out. Now in the US it is generally estimated that there are between 3 million and 6 million illegals; former Immigration Commissioner Leonard Chapman, however, put it as high as 12 million. He said ( 1976) that only one of every three attempting to enter illegally was stopped.

Population on crowded planet Earth (though the rate is declining) should be up to 6 billion by 2000. Who will feed them? By one calculation a quarter of the world already goes to bed hungry. A country doubles population every 20 years if its rate of increase is 2.5 percent. Mexico's is. Mexico City is expected to be the biggest city in the world in a few years. Will they head north?

Three years ago the Controller General told Congress: ''About 62 percent of Mexico's labor force is unemployed or underemployed. . . . A high proportion of the population is under 15; hence population pressure will most likely continue.''

Associate Attorney General John Shenefield also testified, ''In the next 20 years the Caribbean world may attempt to empty out much of its population on our shores as political and economic pressure throughout the area continues to build.''

That's the situation and last week the paper showed lively front-page photographs of illegal aliens, ''walking toward El Paso after crossing the Rio Grande from Juarez, Mexico.'' It would cause excitement if this happened in France, West Germany, England. But in the US Wayne King, the New York Times reporter, quietly observes: ''their number grow dramatically and the Border Patrol concedes that it is all but powerless to do more than hinder the swelling tide.''