President Obama visited Denver on the first leg of a three-day trip to tout economic gains, fundraise and meet with ordinary citizens. Here are some thing to do in Denver when you're president. (Tom LeGro and Natalie Jennings/The Washington Post)

Bears, beer and horse heads: What exactly is going on with the leader of the free world?

On a single day this week in Denver, President Obama scarfed down pizza and drinks with strangers, shot pool with Colorado’s governor and shook hands with a guy on the street wearing a horse mask. His top staffers are promoting these stops on Twitter with the hashtag #TheBearIsLoose — a term one of Obama’s aides coined in 2008 when the candidate would defy his schedule.

More than five years into his presidency, Obama is trying to free himself from the constraints of office, whether by strolling on the Mall or hopscotching the country as part of a campaign-style tour. White House senior adviser Dan Pfeiffer says the president “just wants to get out” and influence “our overall political conversation” by connecting with ordinary Americans.

But to some, breaking free can also look like running away.

Obama’s trip to Colorado and Texas this week took place against the backdrop of a burgeoning crisis on the Mexican border, where tens of thousands of children have been apprehended seeking entry into the United States. In Dallas, Obama dismissed the idea of heading farther south for a border visit as a “photo op” — not long after those photo ops showing him shooting pool and sipping beer in Denver.

Two lawmakers from Texas share their experiences of visiting the overflowing detention centers for illegal immigrants near the Mexico border. They are urging President Obama to visit the border and see the conditions firsthand. (Theresa Poulson/The Washington Post)

House Speaker John A. Boehner (R-Ohio) — who is taking steps to sue Obama for doing too much by executive authority — captured the Republican view of Obama’s travels Thursday when he shouted at reporters: “He’s been president for 51 / 2 years. When’s he going to take responsibility for something?”

Democratic Rep. Henry Cuellar (Tex.) wasn’t much kinder. “If he had time, with all due respect, to have a beer and play pool like he did in Colorado last night, then I think after the fundraisers he should make time to go down there” to the border, Cuellar said Wednesday on CNN.

There are clear benefits to Obama’s outside-the-Beltway road trip strategy. His journey this week has generated positive stories in the local media while allowing him to underscore a broader message that the U.S. economy is getting better.

Obama also defended his decision to eschew a border trip, noting that he is regularly briefed by Cabinet members and aides on the situation and that he has proposed concrete policy solutions. “This is not theater,” he said during an impromptu news conference Wednesday night.

Senior White House officials say they cannot tear up the president’s schedule every time a domestic or international crisis erupts, although they’ve made exceptions before. Last fall, Obama canceled a trip to Asia in the midst of the government shutdown.

“We try to view all of these decisions beyond the immediate feeding frenzy — what decision best helps us achieve our larger strategic goals,” Pfeiffer wrote in an e-mail. “We are always willing to take some short-term press turbulence in the here and now to achieve our goals.”

There are several forces driving Obama’s restlessness, beyond his staff’s commitment to sticking with their schedule. It is clear he has become increasingly frustrated with both GOP opposition to his policies and mainstream news coverage of domestic issues. He points out that Republicans have voted down or blocked every one of his legislative proposals aimed at boosting the economy.

“What I’ve said to my team is ‘Get me out of Washington,’ ” Obama said Wednesday night during a fundraiser in Austin. His summer schedule features out-of-town trips practically every week, including meetings between him and people who have written him personal letters.

The letters are “these thousands of acts of hope from you,” Obama told a crowd Wednesday in Denver’s Cheesman Park. “Cynicism is a choice, and hope is a better choice,” he said.

Pfeiffer said in a phone interview the president is talking directly to Americans about “the issues facing them, doing it in a way that’s compelling and interesting and breaks through a very cluttered landscape.”

The president also seems genuinely impatient with the limitations of his office. He has started walking around D.C. for short stints, referring to himself in the third person as “the bear” as he walks across Lafayette Park or heads to a nearby Starbucks. In Austin this week, he reminisced about the time he roamed free in the Texas capital as a presidential candidate in February 2008.

“The last time I took a walk unencumbered was in Austin, Texas. True story,” he said Wednesday, recalling how the “Secret Service got nervous” and established a rope line in response. “I have wistful memories of that walk.”

A number of impromptu moments on recenttrips have generated just the type of news coverage the White House is seeking. The Denver Post’s front page on Wednesday had a photo of Obama shooting pool with Colorado Gov. John Hickenlooper (D), with the headline, “Obama Sits Down with Coloradans.” Obama decided to start the game after seeing that the bar had a pool table, Pfeiffer said. A photo of him playing also graced the White House’s Web site Wednesday night.

“That’s exactly what you want. There’s no question in my mind that more people will see the images of the president playing pool and sharing a meal with ordinary people than will hear Ted Cruz or Governor Perry criticizing the president for not going to the border,” Pfeiffer said, referring to Sen. Ted Cruz (R-Tex.) and Texas Gov. Rick Perry (R).

It’s also true that many of the Republicans criticizing Obama now for not visiting the border attacked him in 2011 when he did just that.

Still, some elements of the trip — from the unscripted moments to a spate of Democratic fundraisers — have provided easy fodder for the president’s opponents. Republican National Committee Chairman Reince Priebus wrote in an op-ed Thursday in the Austin-American Statesman that “the only way we’ll ever get President Obama to visit the border is to have the Democratic National Committee hold a fundraiser there.”

Senate Minority Leader Mitch McConnell (R-Ky.) delivered a floor speech Thursday accusing Obama of skipping a visit to the border because “he’s decided that there are more important things to do. Like campaigning with Gary Hart and practicing his bank shot.”

“All this continues to make the president look detached from the ongoing crisis on the border,” McConnell added.

Some of the same politicians criticizing Obama now also questioned why he opted to go golfing in Palm Springs, Calif., earlier this year as Islamist militants were making gains in Iraq. Jon B. Alterman, who directs the Middle East program at the Center for Strategic and International Studies, said it’s simplistic to think the president can solve the world’s problems by remaining in Washington.

“I don’t think what this administration needs is more meetings, and I don’t think the president needs to read more briefing papers,” Alterman said.

However, Alterman added, Obama still needs to determine where his personal engagement can make a difference. Sometimes, he said, that individual touch is missing.

“In a world where it’s not yet clear what’s really important, and there’s no real consensus on what’s really important,” he said, “it’s hard for the president to calibrate exactly where to engage.”

Katie Zezima and David Nakamura contributed to this report.