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type of flowering plant, so called from 1690s. In the sense of "person excessively sympathetic" (especially toward those the speaker deems not to deserve it) is attested by 1951, but said by many to have been popularized with reference to liberals (especially Eleanor Roosevelt) in 1930s by newspaper columnist Westbrook Pegler (1894-1969), though quotations are wanting; bleeding in a figurative sense of "generous" is from late 16c., and the notion of one's heart bleeding as a figure of emotional anguish is from late 14c., but the exact image here may be the "bleeding heart of Jesus."
: a bleeding-heart wimpy liberalnoun phrase
A person regarded as unduly softhearted, esp towards idlers who do not merit sympathy •Very commonly used by the politically conservative to condemn the politically liberal
[1950s+; fr religious pictures showing the bleeding heart of Jesus]