Yes, she was very high profile for being a backbencher. Of course part of the reason for that is because she was elected in a special election which received a fair amount of coverage. Did her high profile cause her defeat in the primary?
It was certainly a major factor. A lot of normally Republican voters seemed to consistently break against her, particularly in wealthy suburban areas. She generally did fine in the counties up the river. Obviously her "cowards" remark about the Iraq War was her biggest gaffe, but she the fact that she was very unapologetic about her social conservatism probably turned people off a bit too. She also had some weird election fights with one of her opponents who went after her for refusing to take a stand on the Armenian genocide.
When she actually lost to Wenstrup, I think a lot of Republicans who more or less agree with Schmidt voted against her because they felt Wenstrup could do the job with less drama. He's also a veteran, which is a key distinction as Schmidt was occasionally called a chicken hawk. Wenstrup also ran as something of a Tea Partier to Schmidt's right on a most economic issues. Strangely one could easily paint Schmidt as losing the primary for being too moderate, although I doubt many people would really make that argument given the media characterizations.
