No leader abroad draws more Republican criticism than Putin does. The candidates' message is clear: If any of them are elected president, U.S. relations with Russia will turn even more negative.
"I think it will resonate with Republican voters," said David Yepsen, director of the Paul Simon Public Policy Institute at Southern Illinois University. "There's real concern about what Putin is really up to."
It helps them that the 62-year-old former KGB officer is deeply unpopular in the United States. A survey by the non-partisan Pew Research Center in February said Putin was viewed unfavorably by 70 percent of Americans.
Foreign policy does not always figure prominently in U.S. presidential elections. The quadrennial vote often hinges on the health of the U.S. economy. Republicans this time have seized on the daily drumbeat of news around the world: Islamic State beheadings in the Middle East, Chinese claims to disputed waters, Russia flexing its muscles.
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Given the turbulent state of affairs, Republicans believe the "Putin as boogeyman" theme serves well as a way to rally the party's base of supporters.
In Moscow, Kremlin spokesman Dmitry Peskov said Putin could take the heat so long as the criticism did not go "beyond the limits of what is reasonable, if it's not an insult."
"Unfortunately, for probably the whole of modern history we have seen bilateral Russian-American relations being made a sacrifice on the altar of the election campaign, and being used as one of the tools of the campaign," Peskov said.
'Twitch a little'
Jeb Bush, soon to announce his presidential campaign, says he would like to make Putin "twitch a little." He will reinforce his message of a more strident foreign policy toward Russia on a trip this week to Germany, Poland and Estonia.
Another candidate, former Hewlett-Packard Chief Executive Carly Fiorina, calls Putin a "bad dude." She boasts of having sat face-to-face with Putin in 2001 to bolster her claim to having foreign policy chops.
Putin was the only leader outside the United States that former Texas Governor Rick Perry mentioned in his presidential candidacy announcement speech on Thursday.
"Vladimir Putin uses energy to hold our allies hostage," he said. "If energy is going to be used as a weapon, I say America must have the largest arsenal."
Republicans link their criticism of Putin to the foreign policy record of Clinton, who as the chief U.S. diplomat carried out Obama's "reset" in relations with Moscow in 2009, soon after Obama succeeded George W. Bush as president. They say Obama and Clinton eased up on Putin when they should have applied more pressure.
"She's the one that literally brought the reset button to the Kremlin," Perry said in April.
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Republican candidates generally favor increasing economic sanctions on Russia, sending arms and economic aid to Ukraine, boosting NATO defenses, especially in Poland and the Baltics, and increasing U.S. exports of natural gas to ease European dependence on Russian gas.
Obama has imposed a series of sanctions on Moscow in coordination with European allies, but he has stopped short of massive retaliation out of respect for European concerns that being too tough could trigger Putin's retaliation.
Relations with Russia were strained under President Bush, but Putin's actions and the reactions of Obama and Europe have brought about the worst East-West tensions since the Cold War. Nothing has worked to dissuade Putin, who seems indifferent, bemused and perhaps even politically invigorated by the denunciation from the West.
"The president is afraid of provoking Vladimir Putin," Senator John McCain, the 2008 Republican presidential nominee, told Reuters. "Vladimir Putin is on the move because he has paid no price for his aggression."
Campaign foreign policy advisers say Putin is singled out as a way of separating him from the Russian people, who may or may not share their leader's world view.
"It is better to tactically single him out than to blame 'nasty Russian policy,'" said John Herbst, a former U.S. ambassador to Ukraine who informally advises Republican candidates. "That way you don't have to alienate the whole country."
Michael McFaul, who was Obama's first-term U.S. ambassador to Russia, said the Republican argument is faulty in that the reset led to some tangible benefits: A new nuclear arms control treaty, sanctions on Iran, the opening of supply routes for U.S. forces in Afghanistan.
Having said that, however, he said that singling out Putin for criticism is justified because Russia took its aggressive turn when Putin returned as president in 2012, succeeding Dmitry Medvedev.
"We had a period of cooperation with the Russians several years ago," McFaul said. "We're now in arguably one of the most confrontational periods we've been in since deep in the Cold War."