There is no debate within the Obama Administration on whether to support Israel or not, mainly because there is no one within there who supports Israel. The only debate is which Anti-Israel terrorist group to support, Fatah or Hamas. That is because the civil war between Palestinian Arab terrorist groups, Fatah and Hamas, isn't just taking place in Gaza and the West Bank, but also within the foreign policy establishment.
Unlike the actual civil war, no one is being thrown off buildings or shot in the head, rather there are position papers and fierce behind the scenes debates. The split falls roughly between along ideological lines between the Clinton Administration veterans and some of Obama's new radicals. Between liberals and the hard left.