Israel has stated that it's goals in the current conflict is to stop Hamas from firing rockets at Israeli (technically the rockets even don't land into Israeli territory as it is legally not part of the UN recognized borders). The retaliation is grossly disproportionate and the random killing of civilians especially children is unacceptable. Unacceptable is also the humanitarian disaster caused by the UN suspension of deliveries within Israel fired on an Israeli approved UN contractor killing the driver. The stated goals look impossible to achive unless forcing control of the borders is introduced, something Hamas won't accept. The problems is that Hamas is an unrecognised hardly legal organisation too.
Israle has run afoul with the international oppinion after accusations about the herding of civilians in a building and blasting it and the apparent neglect of children left alone without care to stay by there dead or dying mothers in view of the Israeli soldiers while the Red Cross was prevented by the same army from entering the area.
The USA has adopted an unconvincing position that Israel has the right to defense yet halfheartedly supported a lame UN move towards a cease fire.
Understandably the Security Council resolution didn't impress the main culprits to the conflict and they continued the massacre of civilians. Still it will be harder to convince the American taxpayer that it's OK to spend billions of US money on military aid to Israel only to help the latter condict unefficient campains with disproportionate civilian casualties.
There is widespread understanding that the Arab countries don't support Hamas and even find the current conflict dangerous as it inspires the extremists in their own countries with Iran as the only remaining sponsor.
No wonder the Security Council resolution is a waste of words and my and your tax money as it is concocted without the agreement of the main participants and their sponsors Iran and the USA respectively. The Americans actually took part in the discussions only to abstain in the voting thus sending the right signal to Israel: ignore.
The UN has called for an investigation of war crimes and that I think can be a step in the right direction. A "Balkanization" or "Yugoslavization" of the Israeli conflict consisting of two steps: 1 Foreign occupation of the region by peacekeepers preferably from Europe (but not Turkey) and 2 Arrest of the suspects an international trial to discover guilty for the war crimes. That should satisfy the international community, especially the USA and above all the people of Israel and Gaza (and Lebanon) who won't fear for their lives.
Unfortunately the most probable development will probably be a half-cooked ceasefire leaving open the possibility for future Hamas rocket attacks and Israeli reprisals that plays in the interests of the corrupt militant elements in both Hamas and Israeli government.
What could the new administration do?
Talk to those responsible. It may be hard to talk to Iran but the Russians might help. Next is to decide what America really wants from Israel and ask nicely. I'm sure they won't say no.