the notion they hang around plotting to undermine the US
That's actually not the meter, I've never seen or heard that accusation. It comes across as Alinsky-inspired, lie about the opponent's position.
What I DO know is Trump's idea of it which he gets from being an Alex Jones acolyte - that the "deep state" within the government has orchestrated attacks and events throughout history. This includes the bombing of the Oklahoma City federal building, the massacre at Sandy Hook (he claims that many of the parents were actors), the Boston Marathon attack, and on and on, including believing that the 9/11 attack was "executed by the United States government." Roger Stone is also a major influence. Stone has written several books which center on conspiracy theories, and blames Lyndon Johnson for the death of President Kennedy, and alleges that Ted Cruz's father was involved in that assassination.
Trump actually believes this nonsense, and also believes this same "deep state" has been working from Day One to undermine HIM. Not the US itself. That's his view of it.
For myself I've been reading Miles Taylor's book, "A Warning" and if you don't know who he is, he came out last month identifying himself as the "anonymous" writer of the op-ed piece in the NYT "Part of the Resistance" which Trump hailed as proof of his "deep state" worldview. When actually it appears Taylor was sincere in his writings both anonymously and for his book which I think everyone should read and give a fair shake.
There is NO doubt a "deep state" exists and I believe it actually started with the Civil Service act of 1871, created to limit the power of the President - Prior to 1871, the president could select federal employees, all of whom served at the pleasure of the president. This is no longer the case. I believe this entrenched bureaucracy continues beneath the federal government, controlling and frequently reshaping policies. It's the buffer we need in the event we elect a crazy man to our highest office. It's something we needed and still have, and it's not necessarily detrimental. Call it the swamp, the deep state or whatever you want. It's a CHECK on the Executive.
It is nearly autonomous and is somewhat insulated from executive action and draws power from the national security and intelligence communities, a realm where secrecy is a source of power. This power was greatly increased for the U.S. intelligence community since the September 11 attacks and has essentially built a fourth branch of the U.S. government.
When people of good conscience act, it's not always malevolent. It's fair to say most of them act for the good of their country. It's also way fair to say that there are partisans and hacks of all stripes, inside of it who may act accordingly, as hacks. It's the nature of any bureaucratic beast no matter who the temporary resident of the White House is.