The modernisation of an antiquated economic system implied abandoning the state intervention that had stood Mexico in good stead for several decades but had outlived its usefulness. But it quickly became clear that the new, free-market model needed a social component if it were not to exacerbate the growing discontent and disillusionment that had marked the six-year term of Mr Salinas's predecessor, Miguel de la Madrid.
This reached its most embarrassingly public expression in the whistling and jeering that drowned out his speech at the opening of the 1986 World Cup.
If Mr de la Madrid's term had seen the nadir of the presidency's public esteem, it was Mr Salinas's job to halt the decline. That he has managed to do so is thanks in no small measure to the success of the Solidarity programme, known as Pronasol, which was launched at the end of 1988.
The aim of this public investment scheme is to improve the lot of the millions of Mexicans who, despite the rapid economic growth of the past few years, still live in abject rural and urban poverty. Average real income has actually declined by 15 per cent since 1988, as the reductions in public expenditure have hit the worst-off.
The programme has concentrated its efforts on local public works projects, such as piped water and drainage, paved roads, small bridges and irrigation channels - but has used local organisations and voluntary labour to channel the resources from central, state and municipal governments. The budget for this programme has increased from an initial USdollars 500m ( pounds 256m) to dollars 2.2bn ( pounds 1.1bn) this year, and officials can provide impressive statistics on the number of projects completed.
But what really sets Solidarity apart is the political pay-off it has brought: Mr Salinas and his government have gained enormously in popularity in precisely those areas where his predecessor's administration had lost out: among the poor, the marginal and the migrants.
Critics of the Solidarity programme, such as the political scientist, Jorge Castaneda, and Federico Reyes Heroles, editor of the magazine Este Pais, point to its blatant political and manipulative purpose. Opponents and apologists alike tend to cite the example of the Chalco shantytown on the remote outskirts of Mexico City.
In 1988, Mr Salinas, the PRI's presidential candidate, almost lost the election to a group of dissidents who only a few years earlier had left the party to form the opposition PRD, with Cuauhtemoc Cardenas, the son of an old revolutionary hero, at its head. In Chalco, as in other marginal areas, the PRD swept the board in 1988, and Mr Salinas was prevented by popular opposition from campaigning there. As soon as he was installed in office, public money was poured into Chalco, which became a Solidarity showpiece - heavy earth-moving equipment emblazoned with the Solidarity logo were shown helping to lay water pipes, pave roads, build schools, and so on. Now, nobody there would dream of voting for the opposition; it has become a PRI stronghold.
So is Solidarity just a cynical vote-buying exercise, designed to crush the opposition under the weight of presidential largesse? Critics point to the subtle use of symbolism, such as the use of the colours of the Mexican flag - green, white and red - in the logos of both Solidarity and the PRI, but Pronasol officials indignantly deny any such intentions.
'Solidarity in its conception is light-years away from old-style Mexican politics,' says Luis Rojas, under-secretary for rural development and Solidarity's most articulate exponent. 'In the old days the government used the political structures, the state governors and their local appointees, to hand out patronage - money, jobs in the bureaucracy, public works - and people paid for these hand-outs with votes.
'That's not what Solidarity is about at all. We aim to motivate people to solve their own problems and make their own decisions. If people come to us with a request, we encourage them to form their own Solidarity committee, independently from the existing political structures, and put in an application.
'They liaise with our people to decide which projects they need and how to carry them out. We just provide advice and expertise when it's needed.'
The local people provide the labour, and Mr Rojas points out that funds are channelled through local government, even in the 200 towns and villages where the opposition is in power.
There are now 82,000 Solidarity committees throughout Mexico, and even its most intransigent critics concede that the programme has brought tangible benefits to large numbers of poor people.
President Salinas has identified closely with the programme, making weekly visits to projects around the country. He has recently elevated responsibility for the programme to ministerial status, putting one of his closest lieutenants, Luis Donaldo Colosio, former head of the PRI, in charge.
Clearly, much depends on the quality of the officials running this arms-length form of officially-sponsored local development. Those I saw in action in the state of Morelos, south of Mexico City, were of the highest calibre: hard-working, dedicated, competent and superbly led by an experienced public official, Alvaro Urreta. They were obviously respected by the people they visited, and were imbued with what one young assistant described as a 'new mystique of public service'.
Mr Rojas points out that Pronasol has only 2,000 permanent officials nationwide, none of them traditional politicians. It has even been said that President Salinas and his advisers have toyed with the idea of using Solidarity as the embryo of a new political organisation, which would replace the PRI.
Some of Solidarity's most enthusiastic officials regard the programme as a virtual alternative to the traditional bureaucracy, a way of circumventing red tape, delay and corruption. But Solidarity's reputation is not uniformly high throughout Mexico. I was assured that in some areas, particularly in the traditional Indian highlands, officials tend to behave much like the familiar political cacique, sitting behind big desks, handing out favours selectively. Some things only change very slowly.