Security Agency contractor Edward Snowden highlight the limits of that approach.
Leaders Obama has wooed - and met recently - were willing to snub the American president.
The cocky defiance by so-called "non-state actors" - Snowden himself and the anti-secrecy group, WikiLeaks, completes the picture of a world less willing than ever to bend to US prescriptions of right and wrong.
• Chronology of events in US web snooping case
Snowden flew out of Hong Kong, the semi-autonomous Chinese territory, early on Sunday after Hong Kong authorities rebuffed a US request to detain him pending extradition to the United States for trial.
Snowden has acknowledged leaking details of highly classified NSA surveillance programs.
Beijing may merely have wished to get rid of a potential irritant in its multifaceted relationship with Washington.
But Snowden's next stop was Russia, a US "frenemy" in which the friend factor has been harder to spot since President Vladimir Putin returned to power in May 2012.
WikiLeaks, which says it is helping the 30-year-old Snowden, said via Twitter that he intended to go to Ecuador, whose government has antagonistic relations with Washington. WikiLeaks defies US to help Snowden
Ecuador's foreign minister, Ricardo Patino Aroca, said, also via Twitter, that his government had received an asylum request from Snowden. Ecuador 'analysing' Snowden asylum request: FM
To be sure, the US government is certain to marshal all of its diplomatic, legal and political powers to return Snowden to the United States, where he is charged with offenses under the Espionage Act and with theft of government property.
The United States has revoked Snowden's passport, sources familiar with the decision said on Sunday.
But Snowden has significant levers of his own, in the form of a cache of NSA secrets of unknown size and scope.
Senator Dianne Feinstein, chairwoman of the Senate Intelligence Committee, said on Sunday that the US government apparently does not know the extent of the secrets taken by Snowden, whose last job was as a systems administrator at an NSA listening post in Hawaii.
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"The only thing I've learned is that he could have over 200 separate items and whether that's true or not, that's what has been relayed to me," Feinstein said on CBS "Face the Nation."
Snowden told Hong Kong's South China Morning Post on Saturday that the United States hacks into Chinese mobile phone traffic and text messaging, as well as Chinese university sites that host some of the country's major Internet hubs.
It is unclear whether such revelations played a role in Hong Kong authorities' decision to let Snowden depart, despite the US request to detain him and begin extradition procedures.
Privately, US officials say they believe Beijing authorities made the call to allow Snowden to leave.
In doing so, the Chinese may have simply been passing along a "hot potato," that could have grown into a diplomatic spat.
• Snowden could be useful to us: Chinese newspaper
"For China, this is certainly a bit of a relief. They don't want to let him stay there for a prolonged stay," said Cheng Li, an expert on Chinese politics at the Brookings Institution, a Washington think tank.
"If things get out of control (with Snowden) that will certainly undermine any achievement made in the summit in California, so China is probably very happy that Russia will be the main target," Li said, referring to the meetings between Obama and Chinese President Xi Jinping earlier this month.
Obama, who took flak in recent months over the Internal Revenue Service targeting of conservative groups and Justice Department subpoenas of media phone calls in other leak cases, has so far not faced major criticism of his administration's handling of Snowden.
Most US lawmakers' ire has been directed at Snowden himself, as well as the systems that permitted him to get a sensitive job with contractor Booz Allen Hamilton (BAH.N) and make away with evidence of some of the US government's most shielded intelligence programs.
But US Representative Peter King, a frequent Obama critic and Republican who sits on the permanent select committee on intelligence, said the president should be more aggressive in defending the surveillance programs that US officials say have thwarted terrorist attacks, and more assertive with foreign partners.
"I find it troubling that the president has been so quiet on this. And again, I'm not saying he can control it, but there should be more of a presence including defending the NSA program," King told CNN.
• Hong Kong failure to arrest Snowden 'troubling': US
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"It just seems as if we're adrift right now and I think that these countries are taking advantage of it.
"This is definitely a diplomatic hit at the president, at the US, but as Americans we have to support the president."
If Russia allows Snowden to continue on his journey toward Ecuador, it could wipe out what is left of Obama's policy, dating from 2009, of trying to "reset" relations with Moscow after they turned chilly under his predecessor.
Washington and Moscow have clashed recently over Russia's human rights, adoption by Americans of Russian orphans, missile defenses and, most consequentially, the civil war in Syria.
A photograph of Obama and Russian President Vladimir Putin at last weekend's G8 summit, their hands clasped and staring unsmilingly into space, caught the mood of US-Russian relations.
• Snowden should not be allowed to travel: US
"What's infuriating here is Prime Minister Putin of Russia aiding and abetting Snowden's escape," said New York Senator Chuck Schumer, like Obama a Democrat.
"The bottom line is very simple. Allies are supposed to treat each other in decent ways, and Putin always seems almost eager to put a finger in the eye of the United States, whether it is Syria, Iran, and now, of course, with Snowden."
"That's not how allies should treat one another, and I think it will have serious consequences for the United States-Russia relationship," Schumer told CNN's "State of the Union" program.
• Americans say NSA leaker Edward Snowden should be prosecuted: poll
• US NSA chief says doesn't know how agency failed to stop Snowden
US Senator Lindsey Graham, a South Carolina Republican, sought to keep the focus squarely on Snowden.
"He compromised our national security program designed to find out what terrorists were up to. So, the freedom trail is not exactly China, Russia, Cuba, Venezuela," Graham told Fox News.
"So, I hope we'll chase him to the ends of the Earth, bring him to justice and let the Russians know there will be consequences if they harbor this guy," he said.
While Snowden has garnered raving support on Twitter, there are some who condemn Snowden leaking NSA's secrets. And then there are those who are simply joking about it. Here's a quick look at what the Tweeple had to say about Snowden: