A guest post from EBoZ because I don't have time to write anything thoughtful:
The "far right" label is beginning to stick to Lieberman. See, for example, today's NYT which characterizes him as "ultranationalist," or NPR, AP and CBS who prefer the "far right" terminology.
But what is so far right about Lieberman? The loyalty oath he wants from Arab citizens? Every new US citizen must take a similar oath. Every member of congress must take a loyalty oath every time they are sworn into office. Every first grader in the country does it when they recite the pledge of allegiance.
Lieberman wants to cede Arab parts of Jerusalem to the Palestinian state. Normally, someone who wants to give up sovereignty over united Jerusalem is considered "left wing". He also wants to cede Umm el Fahm which is within the Israeli green line. Umm al Fahm residents are up in arms at the very thought of joining a Palestinian state, (while at the same demonstrating in
favor of Hamas).
The buttonholing of Lieberman into the far-right camp is part of the media's desire to oversimplify a nuanced election platform while at the same demonizing a large Israeli constituency.