The pattern is "I'd as soon X as Y", which means that the speaker would just as readily do X as do Y, often (as here) in the sense that X is undesirable, and Y is equally undesirable.
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The pattern is "I'd as soon X as Y", which means that the speaker would just as readily do X as do Y, often (as here) in the sense that X is undesirable, and Y is equally undesirable.