In the Zocalo, in the heart of Mexico City, they chanted "no more blood" and many called for the resignation of President Felipe Calderon, who began the war by using the army against the drug cartels in late 2006.
Some 35,000 people in Mexico have been killed in drug-related violence since then. Even as the crowds chanted, news came in of another 59 bodies discovered in mass graves in Tamaulipas state.
In the words of poet-journalist Javier Sicilia, who inspired the demonstrations after his own son was killed last week, the war is "tearing apart the fabric of the nation".
But what does he know? In fact, the United States and Mexico claim to be on the brink of winning the war on drugs.
At an international conference in Cancun Michele Leonhart, head of the United States Drug Enforcement Administration, said "It may seem contradictory, but the unfortunate level of violence is a sign of success in the fight against drugs."
She presumably means that all the Mexican drug-traffickers will be dead soon and that nobody else will be tempted by the easy money to take the place of those who are killed. Americans will then stop using drugs because they simply aren't available, or at worst they will be so scarce and expensive that only the very rich can afford them. And we'll all live happily ever after (except the very rich, of course).
There’s a small problem with this theory. Drugs in the United States have become cheaper, stronger, and more easily available over the past 40 years; despite annual claims by the DEA that victory is at hand. To go on doing the same thing every year for 40 years, while expecting that next time will have a different outcome, is sometimes seen as evidence of insanity. We shouldn't be judgmental though.
We could try to be rational for a minute. Former Mexican president Vicente Fox has been doing well on the rationality front recently.
Last August he wrote in his blog: "We should consider legalizing the production, sale, and distribution of drugs. Legalization does not mean that drugs are good. But we have to see it as a strategy to weaken and break the economic system that allows cartels to make huge profits, which in turn increases their power and capacity to corrupt."
This would mean that Mexican drug-users could get any drugs they want, of course. Just like now. The only differences would be that the drugs, being state-regulated and taxed, might cost slightly more and there would be fewer deaths from impurities and overdoses. It wouldn't actually break the power of the cartels as long as drugs remain illegal in the huge American market.
Former Colombian president Cesar Gaviria addressed this issue head-on in a recent interview with Time magazine: "US drug policy has failed. So please, change it. Don't force us to sacrifice thousands of lives for a strategy that doesn't work simply because American politicians lack the courage to change course."
Well said, but why did these men not act when they had the power? One answer is because they were afraid of the American reaction.
The United States has repeatedly made it clear that it will inflict grievous economic pain on any Latin American country that defects from its war against drugs. That is becoming an empty threat, however, for US economic power is nothing like it used to be, even in Latin America.
That's partly because of the recent near-collapse of the US economy, but it's also the result of the rapid growth of the Latin American countries. Mexico, for example, is a rising industrial power with tens of millions of educated middle-class people and an economy that's growing at 7 per cent a year.
It can now say no to Washington without being crushed. It is the American refusal to allow its consumers legal access to the drugs they want that creates the demand and American weapons that arm the Mexican gangs that compete for that market.
Since no American politician will commit political suicide by advocating gun control or the legalization of drugs, Mexico can only escape its agony by refusing any further co-operation with the US Drug Enforcement Administration.
Ending the war on drugs in Mexico would not instantly stop the killing, most of which is between cartels competing for control of the routes by which drugs transit Mexico on their way to the United States.
Just ending the army's involvement would greatly lower the level of violence and legalizing drugs in Mexico would diminish the epidemic of corruption too. You don't need to bribe officials if the drug trade is legal.
The current wave of demonstrations against the drug war is only a start. The policy won't change as long as Calderon is president as too many people have been killed for him to repudiate it now.
But by the end of next year he will be gone and his successor, from whichever party, will be free to change the policy. One of these days, Mexico will just say "no".