WASHINGTON » Sen. Mark Begich, D-Alaska, asked President Barack Obama’s administration for a little favor last month. Send our new interior secretary this spring to discuss a long-simmering dispute over construction of a road through a wildlife refuge, Begich asked in a letter. The administration said yes.

Four weeks later, Begich, who faces re-election next year, ignored Obama’s pleas on a landmark bill intended to reduce gun violence and instead voted against a measure to expand background checks. Obama denounced the defeat of gun control steps on Wednesday as "a shameful day."

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

The trip will also reinforce for Begich and his colleagues a truth about 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 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," Dallek said.

"Obama has this more reasoned temperament," he said. "It may well be that it’s not the prescription for making gains. It raises questions about his powers of persuasion."

Some supporters said the imperative of the moment requires more force from Obama. "He needs to turn up the heat every way he can and every chance he gets because it’s not political points or poll numbers that are at stake but lives," said Rep. Carolyn B. Maloney, D-N.Y., who has sponsored a gun control bill in the House.

The White House on Monday defended the president’s efforts on the gun legislation, saying he had made a vigorous effort to lobby wavering senators. "He made numerous phone calls and had numerous meetings," said Jay Carney, the White House press secretary. "And his entire team here engaged in this process completely and thoroughly."

But the president has long struggled to master his relationship with Congress. During his first two and a half years in office, he favored what aides called an inside approach, working quietly in back rooms to convince lawmakers of the logic of his position. That worked better when Democrats controlled both the House and the Senate, and he passed landmark legislation to expand health care, regulate Wall Street and spend hundreds of billions of dollars to stimulate the economy.

After Republicans took control of the House in the 2010 midterm elections, Obama grew exasperated by talks that rarely seemed to lead to deals. As a result, he adjusted to a so-called outside strategy aimed at using campaign-style rallies around the country to put pressure on lawmakers. That won him victories on a payroll tax cut and student loan rates, but when he tried it on gun control, it failed.

"There have been very few consequences for those that defeat the legislation, and that’s what allows the legislation to be defeated," said former Sen. Byron L. Dorgan, D-N.D., who retired in 2011. But 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."

Bill Daley, who was Obama’s chief of staff from 2011 to 2012, is an advocate for a more robust use of presidential power. He wrote in The Washington Post that Democrats must find a way to punish members of their party who voted the wrong way.

"So I’ll have some advice for my friends in Chicago, New York and Los Angeles: Just say no to the Democrats who said no on background checks," Daley wrote.

White House officials insisted the president had mobilized the full weight of his office to wage a public campaign on behalf of the gun legislation. The president deputized Vice President Joe Biden, a veteran of past gun control battles, to lead the public effort. Behind the scenes, outreach and coordination were managed first by Bruce Reed, Biden’s chief of staff, and later by Denis R. McDonough, the president’s new chief of staff.

Not counting dinners that Obama held with senators, White House officials said he and Biden participated in more than 45 calls or meetings with 30 senators in March and April.

"I don’t know how he could have been more all-in than he’s been," said Dan Gross, the president of the Brady Campaign to Prevent Gun Violence.

Some Democrats on Capitol Hill agreed, saying that Obama’s reputation for not imposing discipline had more to do with the current nature of legislating in Washington, where the two parties have grown increasingly polarized. Several also noted that presidents can no longer use earmarks — the pet projects of legislators that are now banned — to help grease a bill’s passage.

"President Obama is not Lyndon Johnson, and this is not the 1960s," said Rep. Mike Thompson, D-Calif., chairman of the Congressional Gun Violence Prevention Task Force. "It’s a different time and different people, and everyone has their own way of doing things. This president can be every bit as convincing as any president before him."

Obama’s former campaign operation has already pledged to go after Democrats who opposed gun control. In angry remarks after the gun legislation died Wednesday, Obama hinted that retribution might come after all. "If this Congress refuses to listen to the American people and pass common-sense gun legislation, then the real impact is going to have to come from the voters," he said. In the case of Begich, though, it is unclear whether Obama will punish him, and to what end. The administration has not yet committed to approving the road in Alaska that Begich favors and could still block it in the end. And yet, the president also wants to keep a Democrat in Alaska to help hold onto control of the Senate.

"It certainly is the 64,000 question," Dallek said.