Calling Livni a rising star is like calling Wil E. Coyote the sharpest knife in the drawer. Israel needs a modern King David and it looks like what Kadima has to replace Tweedledum Olmerde is Tweedledee Livni.
Kadima is the last line of defense for the always-fractious (but moreso than usual) Israeli polity; the fact that Kadima arose in the first place (from scratch) shows how much upheaval is going on. Livni might get in, but there are other contenders (at least two within Kadima).
If Israel were in lullaby mode, as it was prior to the 1973 war, it would really be in much worse trouble; while those Arab/Muzzie missiles continue to fall from time to time, there’s no way negotiations will have majority support.
If Israel were to completely clean out the so-called West Bank and Gaza, the missiles wouldn’t stop, the launching sites would move. What is needed (unfortunately) is another major (and short) war, during which Israel could take care of the problem right up to its source (Damascus and southern Lebanon).