...Because they tested G‑d, saying: "Is G‑d among us, or not?" Then came Amalek, and waged war with Israel in Rephidim (17:7-8)
After all that they had seen G‑d do on their behalf — the Ten Plagues brought upon Egypt to free them, the splitting of the sea, the "bread from heaven" that descended each morning to nourish them — how could the people of Israel possibly question, "Is G‑d amongst us or not"?
But such is the nature of doubt. There is doubt that is based on a rational query. There is doubt that rises from the doubter's subjective motives and desires. But then there is doubt pure and simple: doubt that neutralizes the most compelling evidence and the most inspiring experience with nothing more than a cynical shrug.
Amalek is the essence of doubt, of irrational challenge to truth. (Thus the Hebrew word Amalek has a numerical value of 240 — the same as the word safek, "doubt"). Because the people of Israel had succumbed to the Amalek within their own souls, they became vulnerable to attack by Amalek the nation.
(The Chassidic Masters)
What is the incident (of Amalek) comparable to? To a boiling tub of water which no creature was able to enter. Along came one evil-doer and jumped into it. Although he was burned, he cooled it for the others.
So, too, when Israel came out of Egypt, and G‑d split the sea before them and drowned the Egyptians within it, the fear of Israel fell upon all the nations. But when Amalek came and challenged them, although he received his due from them, he cooled the awe of the nations of the world for them.
(Midrash Tanchuma)
It came to pass, when Moses held up his hand, that Israel prevailed; and when he let down his hand, Amalek prevailed (17:11)
Did then the hands of Moses wage war or break war? Not so; but so long as Israel looked upwards and subjected their hearts to their Father in Heaven, they prevailed; and when they did not, they fell.
(Talmud, Rosh Hashanah 29a)