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If phone lines crossed because of a little rain, Japan would be in big trouble, wouldn't it.
Literal
Rain [about-くらい] [with-で] phones [subject-が] cross-line-[if-たら] Japan [such-as-なんて] big-trouble is [confirmatory-ね].
A casual, slightly sarcastic observation. くらいで ('just with X,' 'with no more than X') marks a condition as trivially small — 'for such a little thing.' The contracted ~たら from ~てたら (~ているたら) is colloquial for 'if [ongoing state] were the case.' なんて is a dismissive/exclamatory topic marker, 'such a thing as X,' 'the likes of X,' often carrying a nuance of disbelief, contempt, or wonder — here it flavors 'Japan' with 'a country as reliable as Japan.' The final ですよね seeks agreement with mild emphasis.