If Clinton is considered to be Secretary of State, it's going to validate those who argued that there really was not much daylight between the two of them in the primary. She's a relatively hawkish Democrat whose policy decisions under the Bush administration were not good, and they tended to disagree on the role of diplomacy, but their voting records on Iraq were identical. That said, under a Democratic administration, both Clinton and her husband have the ability and credibility to work on the Israeli government and push it towards peace. I'm not up to date on Israeli politics so I don't know how possible this is, but domestically Americans are ready. While I often describe AIPAC as a problematic organization, what its rival J Street has really done is to broaden and diversify what it means to be pro-Israel.
If Hillary Clinton becomes Secretary of State, one of the bright spots of the Clinton legacy - the attempts at Oslo - would be something a good number of decision-makers are hoping she and her husband will continue. I do not think that Clinton would have domestic problems were she to push for a liberalizing policy in the area, since American Jews by and large trust her and her husband. I could see solving this problem as a large area of alignment between Obama and Clinton, and it would very much be in our strategic interest as troops leave Iraq, and it would be useful to have a firm American hand ensuring Israel doesn't do anything crazy should right-winger Netanyahu win the Israeli elections in 2009. Every President tries to solve this problem the last year they are in office, and it never works.
Putting Clinton on the task would change this dynamic and allow for a big personality to work on a big problem she is very well-suited to tackle.