As Barack Obama stepped up to the White House podium on Wednesday morning, to announce the most comprehensive effort in a generation to curb America's epidemic of gun violence, a drama was unfolding on the streets of Denver, Colorado.

In a north-west neighbourhood of the city, a man with a gun threatened another man outside a house. The gunman fled in a red Dodge truck, along with at least two other people, and a mile-long chase ensued with a slew of police cars in pursuit, their lights blazing. The chase would end that day, the day of Obama's address, in a shootout that would leave one man dead and four others injured, including a police officer hit in the shoulder.

The weapon that was used was a handgun. Which is telling, because in the 2,400 words that Obama used to make his historic announcement, one word was missing: "handguns".

The president did mention "military-style assault rifles", as well as the "high-capacity magazines" that are often attached to them; and he did also name-check several mass shootings in which such devastating firearms and ammunition had been deployed, from Columbine through Virginia Tech and Aurora to last month's tragedy in a school in Newtown.

But not once did he refer to the weapon that is responsible for most of the carnage that is inflicted on the streets of inner-city America. Every single day an average of 33 people die to the gun – or to express that terrible figure another way, since the massacre at Sandy Hook elementary school on 14 December most more than 1,000 people have been killed at the end of a barrel. And of those deaths, the clear majority are inflicted by common handguns.

"Common" is perhaps not the most apposite description. The modern handgun is a precision weapon, modelled on military predecessors; it is light, easily hidden and capable of rapidly and accurately discharging up to 15 rounds without reloading. It is fearsomely effective at what it was designed to do: killing.

Take the Glock 19, the 9mm pistol that trades on the gun website Armslist for $675. Its Austrian-based manufacturers boast that it has become a gun of choice of security services worldwide, which is certainly true of police forces across the US. What Glock doesn't say is that the firearm has also become a weapon of choice of criminals trafficking drugs and operating in gangs in the most dangerous inner cities of America, from Oakland to Detroit, St Louis and Memphis.

"There used to be a time when there was a distinction between the crude assault pistols used by criminals and the quality firearms deployed by law enforcement," said David Chipman, who retired from the Bureau of Alcohol, Tobacco and Firearms (ATF) last May, after 25 years as a senior weapons expert. "But now there is so much money in the drug trade that the gap has closed between the guns carried by cops and the guns carried by criminals."

Thanks to the obstructive lobbying of the powerful pro-gun group the National Rifle Association, it is impossible to trace the guns used in the 12,000 gun deaths in the US every year. But there are indications of the scale of the problem. Handguns have been wielded in some of the most notorious mass shootings in recent times: the shooters in the 2007 Virginia Tech massacre in which 32 people died and the 2011 Tucson shooting in which six people were killed and Congress member Gabby Giffords was shot in the head were armed with Glock 19s.

But that's just the thin end of the wedge. Of the 543 law enforcement officers who were murdered between 2002 and 2011, the clear majority – 366 – were shot with handguns. By contrast, only 95 were killed with rifles – the firearms that have dominated political discussions since Newtown about revising a federal ban on semi-automatic weapons.

"Right now the problem on the street is the handgun. Police officers are most likely to be killed by handguns, people on the street are going to be killed by handguns," said Chipman, who now advises the pro-gun control alliance of city mayors, Mayors Against Illegal Guns.

Despite the clarity of the statistics, the silence is deafening. It's not just Obama who isn't using the H-word. Handguns were not mentioned by Joe Biden, the vice-president, in his recommendations to Obama for measures to curb the violence, and they haven't featured in the proposals of most gun groups.

'Sacrosanct status'

A customer inspects a handgun at the Blue Ridge Arsenal gun shop in Chantilly, Virginia. Photograph: Sipa USA / Rex Features

The taboo around the subject is a reflection of a hard truth about contemporary America: with 310 million weapons in personal ownership in the US, guns are so pervasive, so woven into the social fabric of the country, that some of the most glaring problems are simply too daunting even to talk about, let alone tackle. Legally, the handgun has been awarded sacrosanct status. The US supreme court has ruled on more than one occasion that under the second amendment of the constitution, Americans have the right to keep handguns in the home as self-protection.

Those rulings have effectively taken discussion of tightening controls over handguns – the Glocks and Sig Sauers, Rugers and Smith & Wessons – off the table. In the absence of that discussion, the focus has shifted to ensuring that such lethal machines do not fall into the wrong hands in the first place.

"Handguns are used in crimes and shootings every day, and we want to see an end to the situation in which millions of guns are getting into the hands of people without any background checks," said Chuck Wexler, executive director of the Police Executive Research Forum.

Wexler pointed out that about 40% of all gun sales in the US currently side-step any FBI scrutiny into the buyers because of a legal loophole that allows private sellers to operate at gun shows or online without any need of a background check on their customers. Studies suggest that 80% of those who have used a firearm in a crime acquired the weapon in this way without any federal monitoring.

Closing that legal loophole would make it harder for criminal gangs to acquire any form of weapon, handguns included. Most gun control advocates believe that a proper system of federal checks on all gun sales is the top priority for the Obama administration as it embarks on its historic struggle to reduce the bloodletting.

But no matter how effective the system of background checks becomes under the new Obama/Biden mission, it would not alter the fact that America is awash with handguns, and their ubiquitous nature has consequences. Dr Gary Slutkin, founder and head of Cure Violence, formerly known as Ceasefire, is one of the rare voices speaking out about this central truth.

"There are more than 300 million weapons in the US, and we have to recognise they are not being forced upon us – the people want them," Slutkin said. "Using guns violently in our inner-city neighbourhoods has become normal behaviour, so we have to ask ourselves: why do people feel they need guns, and why do they use them?"

Cure Violence seeks to reduce street killings by sending in mediators or "interrupters" to dissipate gang disputes. Its work has become famous in the ravaged neighbourhoods, mainly in the South Side, of Chicago, where more than 500 people were shot and killed last year. Slutkin's aim is to try and change not just the law but behaviour, through a public-health campaign similar to the drives against smoking or drunk-driving.

"We need to change people's thinking," Slutkin said, "so that when they have a grievance – their girlfriend has left them, perhaps, or someone has disrespected them – they don't immediately reach for a handgun."

At the end of the Denver shootout, a father out walking near the crime scene with his four-year-old daughter told the Denver Post: "This crazy stuff can happen anywhere. I wonder what kind of world our kids are going to live in."