While Livni won a personal victory the Left was absolutely trounced. The non-Arab left only won 44 seats while the right wing won 65 (60 if you subtract Yahadut Hatorah).
The problem is that the current system of government is completely broken and it will be very hard for anyone to make a stable government.
I don't see any way for Livni to make a government. Let's do the math. Kadima has a grand total of 28. Labor has stated, and this time I think it is true that they are not joining any coalition. However, just for fun let's add them in as well.
28 (Kadima)
13 (Labor)
-----------
41
Livni needs another 20 seats. Lieberman is looking for 3 things:
1. Security issues
2. Civil Marriages
3. Changing the system of government to a Presidential system
In theory Livni can offer 2 and 3 to Lieberman. However, that only gives her 56. She still needs 5 more seats. The only 2 choices are Shas or Yahadut Hatorah. The problem is that if they are in she loses both Civil Marriage and changing the system of government. Neither Shas nor Yahadut Hatorah will agree to either.
Netanyahu will not have an easy time making a government either. Shas and Yahadut Hatorah will have high budgetary demands and he will need to satisfy Lieberman. However it is doable.
The truth is, for the Charedi world this is by far the best option. They will get money and be able to keep the status quo.
The other alternative is Kadima, Likud and either Labor or Lieberman or both. There is no question that Netanyahu would love to make such a coalition. The big problem with that is who will be Prime Minister? Netanyahu clearly has the upper hand as he can form a right wing government. Therefore the only way I see this happening is if Livni agrees to be number 2. For her own political good she should force Netanyahu to make a right wing government and let him fail. She will then be in a good position to win. However, for the good of the country she should join a government with Netanyahu for the sole purpose of changing the system. The current system is completely unworkable and leads to disaster.
