Israel has spent millions trying to win minds abroad, will spend 20X more

No, that's the argument that their propaganda uses to elicit that support. They have been victim of a terrorist counter-attack from the people they oppress and massacre since decades; it lasted 48 hours and resulted in a few hundred hostages taken and 800 civilians dead (many of them probably killed by the Israelis themselves, who have a policy of killing their own to prevent them becoming hostages).

Since then, Israel launched a campaign of total destruction and massacre, with the clear and often stated intent of ethnic cleansing and annexation of Gaza- a campaign that resulted in tens of thousands of deaths and the entire region razed to the ground. Something comparable to what the Nazis did to Warsaw. The idea that the terrorist act by Hamas can justify anything like this is pure folly, outside of Israeli propaganda. In fact their PM is wanted for crimes against humanity. This is not even accounting for the fact that Palestinians, as an oppressed and occupied people, have a right to defend themselves- a right that Israel as the oppressor and occupier doesn't have.