The answer to both of these is their constituency. In order to stay in power, the parties need to move in the general direction of their voters. Democratic voters are more likely to be against the attacks on Gaza and the Palestinians. Republican voters are more likely to be in favor of bombing the hell out of “terrorists.”
Therefore, Democrats are more likely to be swayed towards the side of let’s not support Netanyahu. By that chain, less deaths will occur (addendum: with US help) with the Democrats in power.
Right now, Biden is doing business as usual. Same trades and sales to Israel as the US has always done. Trump though has said that he’d just bomb them to “finish the problem.”
Progress is led by the people, not the politicians.
Millions of dollars also doesn’t hurt.