janbee's answer is correct. The soft pedal on a piano mutes, or softens, the sound. This analogy has been carried over into the language, thus "to soft pedal" means to make something (something not very pleasant) a bit less objectionable. In other words, to "soft pedal" something means to make it more likely to be accepted. For example: a company finance director says to the chairman, "The new building will cost a lot. We'll have to soft-pedal that one at the shareholders' meeting."