BUENOS AIRES -- Shortly after becoming president of Argentina's telephone company, Guillermo Klein toured the aging facilities of the mammoth state-run firm.

Klein knew of the system's outdated exchanges, worn cables and overcrowded networks. But he was not prepared for the cats, several of which leaped out when the lid to a compartment of wires was opened. "At least we chase away the rats this way, so they won't eat the cables," an embarrassed aide told the telephone chief. Klein was not amused.

In the drive to save their debt-burdened economies, South American leaders face no challenge greater than cleaning house at overstuffed public enterprises. These elephantine companies, the products of a past that saw the state as the primary engine of development, dominate the region's economic activity. Performing poorly, burdened with obsolete equipment and bloated by featherbedding, many of the enterprises have been targeted for sale or reorganization.

Argentina's National Telecommunications Enterprise, or ENTel, has become a symbol of state inefficiency and a focus of anger among consumers seeking desperately to connect with the 20th century.

While industrialized countries average more than 50 phones for every 100 inhabitants, Argentina, which was Latin America's most advanced nation half a century ago, has fewer than 10 per 100. Many of the phones do not work. Crossed lines, wrong numbers and overloaded circuits are standard features of dialing here.

Some Argentines have been waiting more than 15 years to get a phone. In desperation, thousands have simply hired black market technicians, dubbed spidermen, to string cables and tap them illegally into existing lines. These pirate wires sway between buildings in bundles over the streets of Buenos Aires.

Foreign holders of Argentina's $52 billion debt often ask why this country cannot reduce a budget deficit that exceeded 7 percent of the gross national product last year. The deficit fuels an inflation rate that in recent months returned to double digits. In reply, government officials point to firms like ENTel.

Deficits of state-owned firms made up 85 percent of the nation's fiscal deficit in 1986. Although Italy, India, France and Spain have more public enterprises than Argentina, their governments spend less in relation to total national output, according to a voluminous study last year by the Foundation for Latin American Economic Research here.

A study by a government auditing agency found that state enterprises in Argentina lack passable financial records, and some -- including the phone company and railroads -- do not even have complete inventory lists.

Since taking office four years ago, President Raul Alfonsin has repeatedly vowed to scale down public enterprises. But after several abortive attempts at reform, his administration is still hamstrung by a large state sector that provides low levels of service. Mail, for instance, is regularly misplaced. Power failures are frequent. The train system loses up to $3 million a day, and port fees rank among the most expensive in the world.

Argentine officials have concluded that future growth depends largely on promoting private initiative and investment. But steps to reduce the government's economic role remain small-scale. The government has sold its minority interests in several small petrochemical plants, granted oil exploration leases to foreign firms in territories formerly reserved for the state oil company, and auctioned off Austral airlines, which services the nation's interior. But plans announced two years ago to sell major steel and petrochemical works have gone nowhere.

The efforts also have produced at least one new state firm -- a holding company to oversee the 13 largest state concerns.

"There is a lot of talk in this government but very little action," said Horacio Boneo, an economist who has studied public enterprises. "There is the feeling that if only you could find the right guy, a kind of Iacocca, you'd have the problem solved. Unfortunately, that hasn't happened here."

Officials now say that privatization may not be the answer for the country's biggest state corporations. ENTel and the other state companies are so unprofitable and inefficient, they say, that investors have little interest in them. Private capital markets are too thin to absorb the giant firms, in any case.

Since potential buyers include foreign companies, officials also are wary of accusations from opposition Peronists of selling off the national patrimony. Nationalist sentiment remains strong in Alfonsin's own centrist Radical Civic Union.

"We don't have a political class convinced of the need to privatize," said Pablo Guerchunoff, a senior economic adviser. "The tradition of statism and nationalism is still very strong in both main parties and will take time to change."

The president's aides worry as well about resistance from powerful union groups that oppose selling state companies. Various protest strikes last year by public employees resulted in a loss of work for the average laborer of 60 eight-hour days, according to a university study.

So instead of privatization, the government is now thinking in terms of deregulation, hoping at least to expose state firms to competition. A presidential decree issued in November removed the barriers that had kept private firms from challenging the monopolies enjoyed by state enterprises in communications, airlines, electric power and other fields.

Under the decree, officials have only 30 days to rule on the acceptability of a business proposal from a private firm. If no response is received in that period, the proposal will automatically be considered approved.

The decree triggered union protests and work slowdowns, led by the State Telephone Co. Employees' Union. Julio Guillan, the union's secretary general, attacked the "demonopolization" plan as a product of insensitive technocrats and greedy international firms. As an alternative, he urged the issuance of ENTel stock, which, he suggested, could be sold to employees and phone users.

Officials, who have threatened to privatize ENTel entirely if phone service fails to improve, say private firms offer the only source of fresh capital for expanding the country's communications network, given the state's financial plight.

ENTel was created in 1946 during a wave of nationalizations by president Juan Peron. The majority of the company's switching equipment dates from that era. It operates electromechanically, which means it is slower and more prone to congestion than modern electronic systems.

Today, ENTel's 2.6 million lines account for more than 90 percent of Argentina's phone network. A private firm that avoided nationalization serves several provinces but its officials, like those at ENTel, complain that government-set phone rates are pegged too low to finance expansion.

The state phone company also has suffered from frequent rotations of senior staff, reflecting years of political instability generated by periods of military and civilian rule. General managers at ENTel have lasted 20 months on the average.

"For each important decision in ENTel," said Nicolas Gallo, who quit in August after eight months as the company's head, "one has to consult the ministers of economy and public works, the secretaries of communication, industry and foreign trade, the director of public enterprises, four unions, the business chambers and some important suppliers."

ENTel's major suppliers, meanwhile, often complain of stifling bureaucratic oversight by inspectors. Phone maintenance has deteriorated as available funds have gone to pay for new lines. The standard wait for phone repairs here is 11 days.

In the late 1970s, when the military governed, Argentina embarked on a phone development program. But it ran into delays and out of money. New plans for hundreds of thousands of additional lines are again on the drawing boards, prompting fierce bidding among Siemens of West Germany, NEC of Japan and Alcatel of France to supply modern switching and transmission equipment.

Some of the pirated cables downtown have begun coming down amid reports that a private consortium of banks, brokers, currency exchangers and other financial market operators are prepared to pay for a computerized downtown network.

But efficiency at ENTel comes hard. A program named Megatel, launched by the Alfonsin administration in 1985, promised new phones in just a few years to 740,000 subscribers who were willing to advance hundreds of dollars for each installation. Megatel is now months behind schedule amid reports of shaky financing, corruption and other irregularities.

"I've long believed that Argentina's economic takeoff depends on achieving something that should be very simple but which has defeated every government that has been elected or has seized power since Argentina began its decline half a century ago," Robert Cox, a former newspaper editor here, wrote recently.

"In reflecting over the reason why Argentina has not been able to make its economic takeoff, I've come to a disturbing conclusion: God cannot be Argentine, because if he were he'd fix the telephones. I have a feeling that with one little miracle -- the transformation of ENTel into an Argentine Ma Bell -- Argentina could quickly become an economic powerhouse."