Five thousand families live in the Irtacalco slum on the southeastern side of this City. More than 60 percent have regular income.

Of those 3,000 families half survive by selling things like shoelaces and peanuts on the city streets. The rest live off friends and relatives.

Most of the residents of the neighborhood were among the more than 2,000 people who arrive in Mexico City each day from the poverty-stricken countryside to look for work and seek a better life.

Yet, according to government figures, nearly half of the city's workforce - that is, those of working age - are unemployed or underemployed. On the national level, more than half of the 18 million workforce is unemployed or nearly so. The workforce is less than 30 percent of the total population of 63 million.

The statistics are mind-boggling. They roll from the tongues of sociologists, economists, planners and journalists with a sound as dry as the hills around the city where the newly arrived residents build their houses of cardboard and string.

The problem is compounded by Mexico's lack of unemployment insurance or welfare program. There is no Mexican equivalent of U.S. job training or placement programs.

Maria Gonzalex, 35, a mother of eight who came to Iztacalco 10 years ago from the state of Micboacan, has received no outside help for her family since her husband's death in a construction accident several years ago.

"When I went to look for work," she said, "They asked me what I could do, and I had to say nothing. The world was closed to me."

Seven days a week, Maria Gonzalez leaves the one-room mud-floored hut where she lives with her children and goes into the city to look for washing and ironing work in middle-class homes. On a good day, she can make about $5.

In the past, Mexico's bordes of unemployed "Marginal people," as they are called, have not posed a serious threat to either the stability or the social conscience of the country.

Today, they are threatening both. Their number has grown so quickly that it is no longer possible to ignore them. In small, but increasingly ominous groups, the landless peasants and jobless urban slum dwellers are organizing to demand what the Mexican revolution promised them more than 50 years ago.

The United States is now pressuring Mexico to plug the unemployment escape valve - the yearly flow of tens of thousands of Mexicans across the Rio Grande to the north.

Since his inaugurationn 19 months ago, president Jose Lopez Portillo has repeatedly indentified the creation of jobs as one of Mexico's highest priorities, calling unemployment "the source of all injustices."

Fortunately for Lopez Portillo, Mexico's awakening to the unemployment problem coincides with the discovery of a potential 120 billion barrels of oil, in the southeast portion of the country.

Lopez Portillo has called the oil boom, from which Mexico hopes to earn $6 billion a year by 1980 "the first opportunity in our history to act in the area of unemployment." He has earmarked the new oil revenue specifically to that purpose.

Although he has yet to explain exactly how the money will be translated into jobs, Lopez Portillo has promised to spell out a plan for the recently organized, but still unfunded, National Employment Fund in his second State of the Union address in September.

There is no shortage of ideas on how to spend the expected new wealth, and officials in Mexico talks of little else these days.

"There are two basic options and each has a lot of pressure behind it. The first is to fortify the traditional econimic policy of the past 25 years. The second group demands a change," said a leading Mexican economist.

The first option, supported by Mexico's pampered and powerful industrialists, calls for continued low public sector expenditures and increased government investment in the private sector.

The industrialists reason that by allowing private industry to accumulate capital through easy credit, low taxes and high subsidies and import tariffs to eliminate outside competition, the government encourages private investment in industry which, in turn, creates more jobs.

At the same time, the promotion of local industries should reduce the amount of expensive foreign goods Mexico has to import.

This has been the model for Mexico's development for three decades. Its success, at least before worldwide recession in 1974, was remarkable. Mexico's growth rate rose, and the industrialists accumulated vast amounts of money.

In other ways, however, the model has been an abject failure.

With high levels of profit assured, the industrialists felt no need to reinvest their savings. With no outside competition, their goods had high price petition, their goods had high price and low quality. As fewer Mexicans could afford to buy local goods, a downward spiral began slowing production and resulting in fewer jobs.

"We found ourselves with a system of production that was totally incapable of providing jobs," said government employment specialist Clara Josidman.

At the same time, Mexico's 3.5 percent yearly population growth rate was among the highest in the world.

With little government money going into the countryside, more peasants poured into the city to seek their fortunes. Today, for every seven Mexicans who enter the job market, only one new job is created.

"Yet the private sector wants another chance. The argument is that it has not received enough support from the government to assume its proper role in the economy," said the economist.

To many of Lopez Portillo's bright young technocrats, these arguments have a drearily hollow sound.

The industrialists, said Industry Minister Jose Andres de Oteyza, "have already had their chance. We believe this particular model has exhausted itself and that it is necessary to reorient it."

The reorientation, which Lopez Portillo has indicated he favors, and which is even supported by Mexico's traditionally conservative labor unions, calls for large government expenditure in labor-intensive government projects such as road-building and public housing, along with massive support of the country's long ailing agricultural sector.

In the private sector, government investment and attractive credit terms would be handed out according to the number of jobs a project creates.

"What we're trying to achieve isn't easy," said Oteyza. "These groups who have had their opportunity reaped both economic and political power from it . . . power that they want to exercise. . ."

But Mexico's industrialists conceivably could do to Lopez Portillo what they did in 1978 to his predecessor, president Luis Echeverria when public expenditure and inflation rose. The industrialists took their money and ran to the United States and Europe. Devaluation of Mexican currency followed and said an economist, "the country nearly crumbled."

"Maybe this wouldn't happen now because once the government has the oil, it conceivably could tell them [the industrialists] to take their money and get lost," he said. "It is a very dramatic change, because its the first time in history, and maybe the last, that the government might not be as poor as its always been."