This strongly ties to a smart Matt Yglesias item today about Chris Christie as a presidential candidate. Yglesias argues, correctly, that Christie’s current strong polling among Democrats will disappear pretty rapidly if he ceases to be the governor of a very Democratic state and becomes a candidate for the Republican nomination for president.
Two caveats are certainly necessary. One is that some of the reputation might stick. Mitt Romney managed to avoid getting a reputation as a conservative extremist no matter what he did on the campaign trail in 2012; if he had run the exact same race that year but had been governor of Utah instead of Massachusetts, and run as a conservative alternative in 2008, his 2012 reputation might have been different. The other is that it’s certainly possible that some part of reputation is really related to something inherent in the politician.
Mostly, however, it’s probably context. And if you can anticipate changing context (say, a Republican from a liberal state about to embark on a national nomination campaign), then it’s easy to predict changing reputation. Republicans who are choosing candidates based on how they’ll play nationally may want to keep that in mind.