The problem with this line of reasoning is that there's a severe lack of evidence for it. Douglas Gibler at the University of Alabama presents a good review of the literature here. Paul Huth (now at Maryland) and Bruce Russett (Yale) analyzed 54 historical cases and concluded, "deterrence success is not systematically associated…with the defender's firmness or lack of it in previous crises." A follow-up study they conducted looking at 58 cases also found little evidence that countries' past behavior had a strong effect on other countries' perceptions of it, especially in modern cases.
The University of Washington's Jonathan Mercer's book, Reputation and International Politics, finds that there is no predictable effect of backing down in crisis. "Because we know that people often explain the same behavior differently, we also know that reputation cannot be a property concept," he writes. "Even unambiguous behavior — such as backing down in a conflict — can generate different interpretations, some of which may yield information about the target's resolve and some may not. There is no a simple correlation between behavior and reputation."
Dartmouth's Daryl Press finds the same thing in his book, Calculating Credibility . For instance, Press notes that from 1958 to 1961, Soviet premier Nikita Khrushchev made a habit of stating that Western control of West Berlin was intolerable, and that he would, if necessary, fight to retake it. He never did, of course. But that didn't seem to hurt his reputation in the West. "A year after the 1961 Berlin confrontation, when the same American decision-makers confronted Khrushchev during the Cuban Missile Crisis, they took his threats very seriously," Press and his colleague Jennifer Lind wrote recently. "Senior U.S. leaders were convinced that Khrushchev would respond to any forceful U.S. act against Cuba with an immediate Soviet attack against Berlin. Four years of backing down had not damaged Soviet credibility in the least."
But how could this be? Are foreign countries really so stupid that they don't look at our past behavior in trying to predict what we'll do in the future? No — they're just smart enough to know that different situations are, well, different.
"When Iran's leaders are trying to figure out if we'll really mess with them if they interfere with tanker traffic in the Strait of Hormuz, they'll ask, 'Does the U.S. really care about global oil flows?' and 'Can the US Navy really keep those sea lanes open?', and the answers are 'Yes, we care deeply,' and 'Yes, the Navy can,'" Press says. "It would be foolish in the extreme to think that our willingness to intervene in a civil war in which we have no allies and no friends is a good indication to how we'd respond to attacks on genuine national interests."
Perhaps the best case for the irrelevance of past U.S. behavior to future geopolitical disputes, though, is that if bluffing really did destroy U.S. credibility, that would make international politics the only kind of competition on Earth that works like that. "In every domain of competition — business, finance, sports, war, games — smart strategic actors use feints," Press says. "Nobody plays chess and adopts the position that, 'Once I move a bishop forward, I'd never move it back.'…Anybody who says that it's bad strategy to bluff has an open invitation to poker night at my house."
So sure, Obama might have been bluffing when he declared chemical weapons a "red line." But who cares? Just because that bluff didn't work out doesn't mean that we should keep calling or raising going forward. Sometimes folding just makes sense.