WASHINGTON – If there were ever a moment that symbolized the difference between the power of public opinion and the strength of a concerted minority, it came Wednesday when the U.S. Senate defeated a bipartisan measure to expand background checks on gun purchases.

By the time the vote took place, the outcome was expected. But the result was stunning nonetheless, as was made clear by the angry reaction of President Barack Obama, who had invested so much capital on getting gun legislation passed after the shootings in Newtown, Connecticut, only to see those efforts crushed on the first real test.

Obama’s description of the Senate vote — “a pretty shameful day for Washington” — captured the moment and summed up the frustrations that many ordinary Americans long have expressed about Capitol Hill, which is that the system appears tilted in favor of blocking action on controversial issues rather than enacting legislation to deal with them.

The proposal to expand background checks to sales at gun shows and online was cosponsored by Sens. Joe Manchin III of Virginia and Patrick Toomey of Pennsylvania, two progun rights lawmakers. It had the support of more than a majority of senators — 54 ayes to 46 nays — and it had the firm backing of the White House.

More significant, perhaps, in a polarized country is that the idea of expanded background checks received overwhelming support across the political spectrum. Nine in 10 Democrats, more than 8 in 10 Republicans and independents, and almost 9 in 10 Americans who live in households with guns backed the proposal, according to the latest Washington Post-ABC News poll. Nearly all of them said they “strongly” favored the plan.

In the ways of Washington, that still wasn’t enough.”If you ever wanted a textbook example of intensity trumping preference, this is it,” said Ross Baker, a political science professor at Rutgers University. “You could have 100 percent of those polled saying they wanted universal background checks, and it would still be defeated.”

Before the vote, the White House website displayed the message: “Now is the time to do something about gun violence. Let’s make our call so loud it’s impossible to ignore.”

But those voices could not overcome the power of the National Rifle Association, the rest of the gun lobby or the procedural obstacles that are common in the Senate. The NRA mounted a campaign to block the Manchin-Toomey compromise and other stringent measures pushed by Obama and Vice President Joe Biden, such as a ban on military-style assault rifles and limits on high-capacity ammunition magazines.

The demise of the two senators’ proposal — the most significant restriction on gun purchases that had any chance of passing — represented a resounding defeat for the president, who had seized on the issue after the massacre in Newtown in December, which left 20 children and six adults dead.

It was a defeat as well for the victims’ relatives, men and women who have walked the halls of Congress and spoken out passionately for action. And it was a defeat for former Democratic Rep. Gabrielle Giffords, who was nearly killed in a 2011 shooting and had joined in the lobbying effort. They were at the White House with Obama and Biden after the vote, a tableau of hopes crushed.

Wednesday’s vote was also another setback for efforts to find bipartisan accord on difficult issues that have resisted resolution.

“The Manchin-Toomey compromise has gone the way of the bipartisan budget commission, the . . . deficit reduction plan and the (budget) supercommittee,” said Sean Theriault, an associate professor of political science at the University of Texas, Austin. Theriault, author of the recent book “The Gingrich Senators: The Roots of Partisan Warfare in Congress,” added that “while it provided glimmers of hope that a bipartisan compromise could be forged in the Senate, in the end, it serves as a reinforcement for how dysfunctional Congress has become.”

Few lawmakers were fully happy with the proposal that Manchin and Toomey put together. Liberals thought it didn’t go far enough. They embraced it, but there were enough grumbles about it that Sen. Charles Schumer, a New York Democrat who has been a leader in the effort to enact new legislation, begged them not to let the perfect be the enemy of the good. In the end, only four Democrats — all from red states — opposed it, including Senate Majority Leader Harry Reid, who voted against the legislation for purely procedural reasons.

What sank the amendment, however, was the near-unanimous opposition of Republicans, who argued that the proposed restrictions would infringe on Second Amendment gun rights. Only four, including Sen. John McCain, backed the proposal.

There seemed no better opportunity in recent years for Congress to pass new gun control measures, given the public outcry after the Newtown shootings. Obama moved quickly, knowing that with each passing day the prospects for congressional action would diminish. He spoke out frequently and tried to rally not just public opinion but public pressure.

Reid, a longtime supporter of the NRA, brought a bill to the floor shorn of the ban on assault weapons and the limits on high-capacity magazines, believing that would offer the best opportunity for the passage of background checks. Manchin and Toomey worked for weeks to develop a compromise that would diminish the opposition from the NRA and draw more Republicans on board.

But members of Congress are mindful of who votes and who doesn’t on hot-button issues and have seen the NRA’s power in past elections. That, and the Senate’s 60-vote threshold, were enough to frustrate the desires of the majority for action.