The government in El Salvador that the Reagan administration has chosen to provide with extensive military aid and political backing is an unstable compromise coalition that has not been able to demonstrate much popular support.

Members of the ruling civilian-military coalition, which has undergone several changes since it came to power in October 1979, often have admitted that without U.S. support to fight the leftist opposition, twist the arm of the extreme right and shore up the weak economy they could not have remained in power.

"The purpose of this regime is not to be popular," said one of its promoters in the U.S. Embassy during the Carter administration. "It is to serve as a transition toward a more democratic government."

However, the continuing political violence, the recent failure of an all-out leftist offensive and steady accumulation of power by the more conservative members of the governing coalition suggest that such a transition may be a long way off.

Two months ago, a senior U.S. official in El Salvador said he believed that then-president Jimmy Carter would not want to leave office remembered as the support of a "genocidal, nun-killing regime" and President Reagan would not want to come in that way either.

But as intelligence reports mounted at the end of last year showing large-scale Cuban and Soviet Bloc suport for guerrillas in El Salvador, first Carter and now Reagan have thrown the weight of the United States behind the Salvadoran government, despite continuing reports that its armed forces are involved in killings of civilians suspected of ties to be left.

As the Reagan administration sends arms to El Salvador and takes the offensive in the propaganda war that surrounds the fighting there, allegations of atrocities by Salvadoran government troops are shoved aside in the face of an "outside threat."

Despite recent disclaimers by State Department spokesman William Dyes, the Reagan administration has given the impression that it will soft-pedal the Carter administration's concerns about human rights, symbolized by its brief suspension of aid contingent on a serious investigation of the murders of four North American churchwomen in November.

The arms and the economic aid that Washington sends to the Salvadoran government may say it through the current crisis and counteract whatever foreign threat exists, but it promises little for the long-range stability of El Salvador or the region.

In the 16 months since its several colonels came to power in a military coup, the current Salvadoran government has remained an unstable compromise coalition conjured up by Salvadoran officers and North American diplomats to forestall what seemed in 1979 to be a widely supported leftist push for power.

The compromise was built in the aftermath of the Nicaraguan revolution as a shortcut to reforms that might avert a similar leftist takover in El Salvador. The government was founded on promises of liberal initiatives, some of which were promoted and even designed by the U.S. Embassy -- and many of which remain to be fulfilled.

There were some hopeful moments in the first months of the government when the military brought in civilian politicians from a wide spectrum of parties. Many were moderate socialists described by U.S. officials as "some of the most capable men in the country." But after less than three months in the government they were forced out, and many joined the cause of the guerrillas under the banner of the Democratic Revoluntionary Front.

While every civilian minister in the October 1979 government has resigned or been replaced, the minister of defense, Col. Jose Guillermo Garcia has retained his post despite repeated abuses and atrocites by his troops.

The most liberal colonel in this original government, Adoldo Majano, was forced out in December and went into hiding. It was announced Friday that he had been arrested.

Christian Democrat Jose Napoleon Duarte, whose party entered the government a year ago, was recently appointed president. But Col. Jaime Abdul Gutierrez, a close political ally of Garcia, retained the position of commander-in-chief of the armed forces, an indication that the military has lost none of its power.

The practice of the U.S.-backed government, although not its announced policy, is a combination of tactics described by Archbishop Oscar Romero, assassinated last March, as "reform with repression."

Large amounts of land have been redistributed in an attempt to break up the near-feudal economic system that for half a century placed almost all the wealth of the country in the hands of a small group of families known as "the oligarchy."

Such initiatives are credited by Duarte and U.S. officials with weakening the popular support of the revolutionary left and causing the failure of its January attempt to mount a popular insurrection.

Government repression, however, remains a concrete reality in El Salvador, and most analysts believe no single fact of Salvadoran life plays more certainly into the hands of the rebels over the long run.

Last year brought unprecendented terror for the Salvadoran people as a shadow war of assassination and retaliation swept the country. More than 10,000 people died, and many reliable sources blamed government forces for most of the deaths. All this was happening despite constant emphasis on human rights by the Carter administration.

Leftist rebels regularly murdered soldiers, their families and friends and even those merely suspected of sympathy to the government. The armed forces, accustomed to complete license under a half century of military rule, moved to exterminate the opposition. Right-wing death squads were equally active. According to the most recent State Department human rights report, many of the right-wing groups have close ties with retired and active members of the armed forces.

Their victims were most often kidnapped, tortued and killed as slowly as possible.

Guerrillas are virtually never taken prisoner after clashes with the armed forces. It is common, to find the bodies of rebels who supposedly died in fire fights but who actually had been strangled.

None of these practices, although officially deplored, has ended.

Part of the rationale behind U.S. military aid to El Salvador, even before the Cuban threat was emphasized, was to help bring the Salvadoran military under control.

The idea was to provide training and equipment to give incentives to the Salvadoran armed forces to abandon their conncections with and dependence on the traditional economic inteests that run the country.

Through training programs such as one begun for Salvadorans last summer at the U.S. military schools in Panama, it was hoped a respect for human rights and more subtle ways of winning the hearts and minds of the people could be instilled.

While such objectives have not been abandoned, neither have they shown any conspicuous success, and they may soon be forgotten as the Salvadoran military consolidates its forces and breaks out its new American guns for an all-out counteroffensive against the guerrillas.

Now that the left's "final offensive" has failed -- and it clearly had failed before the arrival of a single U.S. helicpoter or gun -- many leftists are becoming interested in a negotiated settlement.

The civilians in the Salvadoran government say they want to negotiate a "process" but will not negotiate away the government itself. The Salvadoran Army, with its officers beginning to believe that their license to kill is restored by the Reagan administration, has begun looking forward to a return to business as usual.

If there is no negotiated peace and the most conservative elements of Salvadoran society regain complete control of the government and its soldiers, many U.S. officials who have worked in the area fear that the people who abandoned the left because of the promise of reforms will return to it and the popular insurrection that no amount of outside Communist aid was able to provoke could then begin in earnest.