I don't know whether Vladimir Putin thinks of President Obama as weak, and whether that will encourage Putin to act in ways he otherwise would not have acted.
Obama's defenders (and I am often a defender) discount, somewhat magically, the influence of past events that reflect poorly on this administration while playing up those that implicate other culprits. In Syria, Bashir al-Assad violated an international norm, one that requires serious punishment, and instead, had his toys taken away. Reducing Syria's chemical weapons stockpile is an unalloyed good, but leaving him unpunished is probably a mistake. Ideally, Obama would have figured out a way to do both.
I think the U.S. response has been decent, so far; whether Obama is weak is academic. We go to conflict with the president we have, and he's doing well.
Obama's critics contend that he's not Ronald Reagan, but Reagan, as eager as he was to speak to the moral failings of communism, treated the Soviet Union with more nuance than his ideological hagiographers would suggest. Indeed, by the end of 1983, Reagan grew skeptical of those advisers who urged him to treat Soviet leaders as belligerents, as if they were routinely and only deceiving him — which is to say, not to deal with them directly at all — and instead recognized that in order to advance the cause of nuclear disarmament, he would have to acknowledge that the Soviets had legitimate interests and that those interests had to be recognized.
After the biennial NATO Able Archer nuclear command post exercise in 1983, British Prime Minister Margaret Thatcher, who had no illusions about Soviet deception campaigns, told Reagan that the Soviets seemed genuinely alarmed by what they believed were preparations for a U.S. first strike. U.S. intelligence assessments later concluded that the Soviet reaction to the exercise reflected real fear. That year, a series of incidents proved spooky for both sides, most indelibly the September downing of Korean Air Lines Flight 007, which the Soviets (legitimately, according to classified histories) mistook for a U.S. electronic surveillance plane that was orbiting nearby. Among other things, what scared the Soviet leadership was the fact that the Reagan administration seemed willing to deliberately misstate the facts on the ground, to the world, in order to gain leverage when strategic nuclear arms reduction talks were slated to resume in October. (That, of course, was exactly what the Soviets were doing, regularly, with world events.)
That the U.S. seemed to be matching Soviet deception was very alarming. In general, as former CIA Russia specialist Richards Heuer noted, American political leaders had let the military and intelligence bureaucracies engage in deception and would otherwise keep their hands clean; 1983 proved otherwise. By the time of the exercise, the KGB was frantically cabling embassies around the world, begging for signs of an imminent U.S. first strike.
After Able Archer, Reagan wrote in his diary that "I feel the Soviets are so defense minded, so paranoid about being attacked that, without in any way being soft on them, we ought to tell them that no one here has any intention of doing that."
Within weeks, he had consolidated control of the nuclear portfolio into the White House, and out of the Pentagon. Reagan would never labor under the illusion that the Soviet leaders were telling him the full truth. It confounded him, for example, that Gorbachev would deny the existence of a Soviet strategic missile defense program, even though the U.S. was observing its testing from the skies. But he looked beyond that. He found a way to talk, to negotiate, with people intent on deceiving him. Obama admires Reagan for thinking beyond his present moment. Here is a chance for him to do the same.