NEW YORK — “Mission Accomplished.” “Change We Can Believe In.” “No Child Left Behind.” Sometimes catchphrases for campaigns, policies or political ideas catch on. Sometimes they become fodder for critics and headline writers.

The Obama administration’s pledge to use “smart power” in its foreign policy has been drawing both kinds of responses since Hillary Rodham Clinton first used the term a year ago, during Senate confirmation hearings on her nomination for secretary of state.

Within days, Fox News ran the headline “Clinton’s ‘Smart Power’ Slogan is Just Plain Dumb, Branding Experts Say,” over a story quoting marketing specialists who condemned the slogan, but not necessarily the policy, as “smarmy” and “ridiculous.”

But President Barack Obama’s supporters say smart power is the right term for the right policy — using the whole palette of options to advance American foreign policy interests, instead of what many Democrats regarded as the rush to war under George W. Bush.

“We must use what has been called smart power: the full range of tools at our disposal — diplomatic, economic, military, political, legal, and cultural — picking the right tool, or combination of tools, for each situation,” Clinton wrote on the State Department Web site.

Now both sides are taking the measure of Obama’s first year as a world leader, and giving smart power mixed reviews.

Suzanne Nossel, who popularized the term, says she is “very gratified” to see that the idea has taken hold. Now deputy assistant secretary in the State Department’s bureau on international organizations, she brought the term to wide attention as the title of her 2004 article in the influential journal “Foreign Affairs.”

The list of tools the U.S. could use to achieve its foreign policy goals — from talks, to sanctions, to the 101st Airborne — reads like a primer on international relations. But Nossel says smart power doesn’t just restate the obvious. One of the biggest challenges is getting the complex federal bureaucracy to think as one, she says. When a foreign policy issue needs attention, it’s too easy for departments to favor tools they oversee — military responses from Defense and diplomatic ones from State.

“We’re trying to look at all the tools as part of a single toolbox,” Nossel says.

But for James Carafano, a national security expert at the conservative Heritage Foundation think tank in Washington, smart power is an “empty-headed slogan” used as a sweeping condemnation of Bush administration foreign policy.

“The arrogance of it is ridiculous,” Carafano says. “There’s no analysis. There’s no data… It does not pass the second-grade test.”

He says backers of smart power discount the Bush administration’s use of diverse foreign policy tools, such as coalition-building before the Afghanistan and Iraq invasions, and ignore the fact that U.S. national interests change little when the party in power changes.

NATO backed the U.S. invasion of Afghanistan in 2001 and continues to send troops there. France, Germany and Russia opposed the 2003 Iraq invasion; many leaders who supported the invasion, including the prime ministers of the United Kingdom, Spain and Italy, faced widespread domestic opposition.

Obama didn’t use the words “smart power” in his 2010 State of the Union speech, but he did say that America’s destiny is “connected to those beyond our shores.” He mentioned international cooperation on isolating North Korea and Iran over their nuclear programs, the growing importance of U.S. allies in Afghanistan, and negotiations with Russia over nuclear weapons.

A few conservatives have praised some of Obama’s steps. In a recent article, Gary J. Schmitt and Thomas Donnelly of the American Enterprise Institute credit Obama for making the case that military force is sometimes justified, in his Nobel Peace Prize acceptance speech in December. Francis Fukuyama of Johns Hopkins University supports both the Afghan troop surge and the deadline to begin withdrawal.

But Robert Kagan of the Carnegie Endowment for International Peace charges that Obama has abandoned critical elements of U.S. foreign policy by accepting a decline in American influence relative to China, rather than reasserting U.S. dominance, and by seeking common ground with Russia and China while growing distant from steadfast, democratic allies, such as NATO countries, Israel and Japan.

Joseph Nye, a Harvard professor often credited with coining the term smart power, calls it “nonsense” to say Obama has accepted a decline in U.S. influence on the world stage.

Nye points to the president’s response to the global economic crisis: launching a stimulus package that averted a depression; then convening not just the top economic powers but a larger group, dubbed the G-20, to broaden the recovery and prevent protectionist trade policies. Those steps have shored up U.S. power in all forms, says Nye, co-chair of the Smart Power Commission at the Center for Strategic Studies and a former assistant secretary of defense during the Clinton administration.

“Declinism” — the fear that the America’s global leadership is waning — is a cyclical phenomenon in the U.S., he adds. It comes around after a shock, such as Sputnik, oil price hikes or, this time around, the debt burden to China.

It is too soon to say whether Obama will talk Russia and China into imposing strong sanctions on Iran over its nuclear program, Nye says, but the president has already demonstrated that Iran, not the U.S., is the obstructionist party.

Critics are quick to jump on the catchphrase, says Nye, but he sees the Obama administration’s smart power as a strong plus, and a clear change in direction from its predecessor.

Carafano, however, says Obama offers speeches, not initiatives, and has been forced to admit that many issues are more complex than he had thought. Meanwhile, he says, trying to talk with Iran’s leaders has cost the U.S. the chance to condemn their domestic human rights abuses.

“The most generous thing to say about the administration is that it’s too soon to tell,” Carafano adds.

But Nossel points to progress in her area of expertise — international organizations. Where some Bush officials stridently criticized the United Nations, she says Obama officials have worked with U.N. agencies such as peacekeeping and the Human Rights Council, trying to forge them into effective bodies.

Officials don’t expect multilateral engagement to be a panacea, says Nossel. They take what she calls a “hard-headed view” of what international organizations can achieve.

“When successful, we get agreements that shield us from criticism and mobilize partners” to share challenges, such as rebuilding Afghanistan and Haiti, she says, adding that revitalizing ties with traditional allies is a priority.

Despite the critics who have panned the term soft power, Nossel still sees it as capturing the spirit of the new administration.

“You have a whole set of tools,” she says. “That’s what makes you strong.”