What if Harry S Truman refused to recognize Israel?

Would Israel have survived, or would the Arab armies have dealt a decisive blow to the nascent state?

I don't think US recognition (or the lack thereof) was all that decisive in Israel's victory in 48. What won them the war was better training, better motivation, the various Arab Armies having opposing agendas and surprisingly (given their latter animosity) some East Block weaponry.
 
Truman would be condemned by the Jewish community and many progressives (like Henry Wallace, who were strong supporters of Israel) and this may be enough to swing the election towards Dewey.
 
One can argue that Stalin was at least as important as Truman in the founding of Israel:

"Yes again, Truman did immediately recognize Israel (de facto but not de jure). But he had already enforced an arms embargo on the Middle East, forcing Israel to scavenge for its survival.

"By contrast, not only did the Soviet Union under Stalin vote for partition, and also recognize Israel—the first state to do so de jure, three days after independence—it had come out in favor of a Jewish state well before the United States. Moreover, it had held firm in that support both before and after the vote, and had indirectly assured that the newborn state would have the war materiel it desperately needed to defend itself. According to Abba Eban, Israel’s first UN ambassador, without the Soviet vote in favor of partition (together with the votes of four satellite nations), and without the arms provided by the Soviet bloc, “we couldn’t have made it, either diplomatically or militarily.”..." https://mosaicmagazine.com/essay/2017/11/who-saved-israel-in-1947/
 
Indeed, Henry Wallace and the Left attacked Truman in 1948 for not recognizing Israel de jure and not lifting the arms embargo. Wallace's strong showing among Jewish voters--which cost Truman New York's electoral votes--was of course due partly to leftists who would have voted for Wallace anyway, but some non-leftist Jews also voted for Wallace in protest. (One might ask why in that case Truman wasn't more pro-Israel, why he didn't grant de jure recognition or lift the embargo--and one answer IIRC is that Marshall threatened to resign if he did so...)
 
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