The unmistakable meaning of Schumer's threat is that the intelligence organizations of the United States — and other Western countries — are independent of the rule of law, are unaccountable powers unto themselves.
A Republican leader of national stature who said such a thing would be called upon to explain himself, and could well touch off a vicious round of attacks against the entire intelligence establishment, as happened in the 1970s after Watergate.
Schumer may have been woefully stating the facts, not threatening. He means he was afraid of them, too.
They could say to anyone: we will reveal the private medical records we have showing your daughter was medicated for mental problems and spent in week in a facility. What will her fiancé say and her bosses at her new career now that she’s out of college?
Or, we altered some records to say as a youth you had two DUIs and one shoplifting and were in jail for three days. They look as genuine as Obama’s birth certificate. Can’t prove they’re forgeries, can you? Sort of ruins your political career, doesn’t it?