Dozens of college students murdered in their classrooms; a member of Congress shot at point-blank range; innocents gunned down in a movie theater. Then, in the aftermath of a mass gun crime, the same ritual: national shock and anger, traumatized communities asking how this could happen, followed by . . . nothing. At least, no progress on gun safety.

In a speech to the Urban League on Wednesday, President Obama called for a conversation on youth violence and more steps to keep guns away from criminals and the mentally ill. But everyone, including Obama, has been pretty frank about it: no major new gun laws will result.

However, in Washington, nothing is ever as immovable as it seems.

The key is to understand how intractable problems are ultimately dislodged — not by a single, seismic event, but by a slow shift in politics.

Consider three categories of intractable issues and the forces that have gotten them unstuck.

One reason for paralysis is that politicians fear the consequences of taking on powerful, well-financed organizations such as, when it comes to guns, the National Rifle Association. The gun lobby dramatically outspends gun-control advocates and has a long record of successfully opposing politicians who cross it.

Still, even a heavyweight institution can be sidelined when a problem becomes too large. The AARP has long been regarded as an invincible opponent of Social Security reform. But in the early 1980s, Social Security was nearing collapse. In 1981, the Social Security trustees issued a report warning that the system would be “unable to make benefit payments on time beginning in the latter half of 1982” and that it would run out of money by the middle of 1983. A bipartisan group of lawmakers began to explore the idea of making changes to Social Security, but the AARP stood firm.

A commission led by Alan Greenspan recommended fixes to Social Security in January 1983, and the AARP fought the proposals vigorously. The group argued that rather than change benefits or payroll taxes, Congress should raise other taxes and give that revenue to Social Security. It ran ads and urged its thousands of volunteer leaders to swamp Congress with letters, calls and visits. But the scale and immediacy of the problem moved President Ronald Reagan and congressional Democrats to take on the matter squarely, cut a deal on reforms and put in place a long-term fix.

Sometimes a consensus of experts raises an alarm, but Washington tunes them out. In the case of guns, the experts are police chiefs and mayors in cities plagued with gun crime, who almost uniformly support tougher gun laws, to little avail in Congress.

But expert voices can start to ring louder on Capitol Hill when the data move into the public’s consciousness. In the 1960s, a small band of scientists began to notice the impact of acid rain — pollutants emitted by power plants, most in the Midwest, were being carried by winds to the Northeast, where they were damaging waterways and forests.

This problem was hard for the nonexpert to spot. Only scientists understood that there were rising levels of hydrogen ions in the rain. They saw the trends and understood the significance, even if the public did not — like a minor cough that seems innocuous but to a doctor’s ear could be an early sign of lung disease.

The scientists’ warnings were ignored in the policy debate. No one did anything for more than a decade. But their concerns eventually began to move from academic journals and niche magazines into the mainstream. The public finally took notice of reports showing that many lakes in New England were so acidic, they no longer could support fish and other wildlife. And they connected the dots between lakes in New Hampshire and power plants in Ohio.