While nothing is certain or guranteed until you try to board, or land in Israel, I do have friends who have flown over here and entered on a passport that has less than 6 months validity left to it. You can also try to claim that you called up and were told that you can renew it in Israel.
Something else you might try is to make the claim, if you are jewish that you are eligible to make aliyah (immigrate to israel). Technically if you fit into this catagory you dont need any passport when you get there, as you can apply for aliyah before going through immigration and will get new documents before you leave the airport.
I once had a similar but different issue. I was flying KLM on a one way ticket EWR-AMS-TLV. In AMS I was told that I was being denied boarding, on the flight ot TLV, due to the fact that I only hold a US passport and the rules were that I needed to show a ticket that showed that I was going to exit Israel. I was forced to purchase a one-way return from Israel to the US, fully refundable. When contacting the KLM office in TLV I was given a full refund, including the $35 fee, becuase I could claim that I was indeed able to declare aliyah upon arrival and a return ticket was not needed.
Try contacting the Israeli consulate and see if they can give you a letter stating that you will be ok.