That political elites (publicly) disagree with the public doesn't mean there's a deep state. It just means that your democracy isn't very responsive.
'Deep state' is being thrown around a lot these days. It's proper meaning is in relation to things like Italy's Propaganda Due lodge: a tightly-connected network of people who are in a strong sense anti-democratic, who are not publicly known but have something of a veto over the actions of an elected government.
Some of those features apply to the anti-Trump official world in the US, but only in a much weaker form. And this isn't to do with it, not least because Trump is the one pushing the button.
You're arguing a tautology - unresponsive democracy by definition is when the will of the people is not responded to. Opinions or desires of the people in that case are not correlated with the actions of the state. The state instead responds primarily to the elites. The elites are the deep state.
No, I'm arguing that the concepts of unresponsive elites, and a shadowy deep state, are distinct. The latter is a lot rarer (and, frankly, a lot more sinister) than the former.
The idea that the actions of the state don't correlate with the desires of the people is more-or-less deliberate in a representative (rather than direct) democracy, incidentally. As a political scientist I find it rather offensive that the word 'democracy' has been repurposed to mean a kind of replaceable oligarchy rather than government-by-the-people, but that ship sailed decades ago.
> No, I'm arguing that the concepts of unresponsive elites, and a shadowy deep state, are distinct.
They are distinct but not disjoint; the “deep state” concept is a specific form of unresponsive elite.
> The idea that the actions of the state don't correlate with the desires of the people is more-or-less deliberate in a representative (rather than direct) democracy
No, it's not, in general; the purpose of representative democracy is to allow the actions of the state to give effect to the desires of the people, on the premise that even most people with the requisite ability to effectively decide how to give effect to their desires aren't optimally employed spending all their time figuring out how the state should do that.
It's true that the US federal model of an unusually large number of barriers and unusually undemocratic selection and allocation of representation is designed to prevent government from representing the desire of the people, but the US system isn't the Platonic ideal of representative democracy.
> No, it's not, in general; the purpose of representative democracy is to allow the actions of the state to give effect to the desires of the people, on the premise that even most people with the requisite ability to effectively decide how to give effect to their desires aren't optimally employed spending all their time figuring out how the state should do that.
That's one argument for representative democracy (and, I think, the best one for why participatory democracy is tricky) but it's not the intention behind existing representative institutions, at least in the US and the UK (and the countries who inherited different parts of our systems).
Edmund Burke's address to the electors of Bristol contains one of the most famous declarations of this principle: 'Your representative owes you, not his industry only, but his judgment; and he betrays instead of serving you if he sacrifices it to your opinion.'
The Federalist papers show that the US model was also not designed to operate as an efficient aggregator of citizens' opinions, but more as a means of the public endorsing competent and honest representatives to govern on their behalf.
The classic book-length exposition of this model (which is basically modern elite orthodoxy) is 'Capitalism, Socialism and Democracy', by Joseph Schumpeter. David Held's 'Models of Democracy' is a good comparative text, though there are lots of those to chose from.