The source seems bad, for some reasons they added the 10% of "unsure" to "supports".
"the new survey found 56% of Americans oppose U.S. military action in Iran, while 44% support it."
But later:
"A majority -- 54% -- of Americans disapprove of how Trump is handling Iran. Another 36% approve and 10% are unsure"
36% support it.
They're different questions. One is whether they support the way Trump is doing it. The other is whether they support a war overall.
Their reason for supporting a war but not the way Trump is doing it could range from it being too extreme to not being extreme enough. Some people unironically want nuclear weapons to be dropped and will settle for nothing less.
I missed that, but then it is still not correct to say 44% support the invasion. In a very different framework (clear plan, cooperation with iranian opposition, working exile government, transition plan ..) I also can see myself supporting military action against the religious fanatics in power in Iran. But this invasion I do not support.