Margaret Chase Smith made this statement on June 1, 1950. She did so in response to the claims that Sen. Joseph McCarthy had been making about communists in the government. Basically, she was accusing McCarthy and his followers of conducting a witch hunt. She was saying that they were abusing their powers instead of working (as they were supposed to) to help Americans.
During this time, McCarthy was accusing people (without any real proof) of being communist. He was doing so, many thought, to make himself into an important and powerful national political figure. Smith was calling him on it -- telling him that what he was doing should have been against his conscience because it was simply an abuse of power.