But Mr. Begich’s defiance and that of other Democrats who voted against Mr. Obama appear to have come with little cost. Sally Jewell, the interior secretary, is still planning a trip to Alaska — to let Mr. Begich show his constituents that he is pushing the government to approve the road.

The trip will also reinforce for Mr. Begich and his colleagues a truth about Mr. Obama: After more than four years in the Oval Office, the president has rarely demonstrated an appetite for ruthless politics that instills fear in lawmakers. That raises a broader question: If he cannot translate the support of 90 percent of the public for background checks into a victory on Capitol Hill, what can he expect to accomplish legislatively for his remaining three and a half years in office?

Robert Dallek, a historian and biographer of President Lyndon B. Johnson, said Mr. Obama seems “inclined to believe that sweet reason is what you need to use with people in high office.” That contrasts with Johnson’s belief that “what you need to do is to back people up against a wall,” Mr. Dallek said…

“There have been very few consequences for those that defeat the legislation, and that’s what allows the legislation to be defeated,” said former Senator Byron L. Dorgan, Democrat of North Dakota, who retired in 2011. But Mr. Dorgan said that in the modern era, constituent pressure is the key. “Put some real pressure on back home. The pressure back home is more important than pressure from the White House.”