Woodrow Wilson sprang immediately to mind as an example of a president who effected change despite an intransigent congress. He is also a president who fought against entrenched interests.

Your idea seems to be more of an observation of recent presidents than a property of the presidency itself. I think there are two things that make it so. First, modern presidents are generally picked from a very narrow pool of candidates which the parties and the media help select and shape, thus making sure a relatively docile candidate is chosen. Second, most modern presidents are very politically oriented and beholden to the groups that donated to them during their campaigns.

I think that can be used to describe Hillary, but I think both Sanders and Trump are non-docile and not beholden to outside interests. Sanders, because his funds largely come as a mandate from individuals and he is very clear about who he works for. Trump, because he has nothing at all to lose by doing whatever he wants.

This is kind of sad, when I think about it - what you're describing is Trump and Sanders being opposed to Hillary and <Trump's opposition, I forget the name> in a way that matters just as much as Democrat VS Republican, but that decision is entirely up to the Dem/Rep oligarchy.

Plus both Trump and Sanders bring in a lot of new voters. That may potentially scare the shit out of weaker members of congress... as it should.

The president has an enormous amount of power. The executive branch has been steadily expanding its power since the beginning of the country.

Consider, for example, a Sanders DOJ vs. a Trump DOJ? (I suspect a Trump FBI would be primarily interested in cataloging and spying on anyone critical of Trump or of Muslim faith, essentially use COINTELPRO as a starting point, but make it better and stronger and do good deals). What about a Sanders DEA? EPA? DHS? The executive can do nearly anything if they are bold enough. The executive can ignore the judicial branch ("He has made his ruling, now let him enforce it"), the legislative branch (subpoenas from congress? About illegal leaks of classified information for political purposes concerning Valerie Plame? Please direct the law enforcement officers with weapons in your branch to serve them. You don't have any?)

I believe Sanders would refrain from using executive power to make things worse, while I am certain all of the other candidates would not refrain. Hillary will not differ from Obama nor does she claim to. Trump's shtick is to be an American dictator, an executive strong man who advocates violence and abuse towards anyone who disagrees with him and acts as an outlet for racism and hate and anger. Imagine if he had an army of FBI, DHS, NSA agents at his beck and call.

I've always wondered what would happen if a President gave a TV-broadcast speech, telling people to write to their congressmen and demand a change of their policy on some issue.

Would that be illegal? Would it be speech? It's not like the President would be telling you who to vote for (though it might be different if the US had referendums, because the President would be telling you what to vote for); the President is simply attempting to sway your opinion, and then telling you to inform someone else of your (hopefully swayed) opinion.

This is exactly what I think Trump has in mind. First time congress doesn't do what he wants, he'll get on TV and list off every single congress critter that is getting in the way of Making America Great Again. They'll quickly fall in line or find themselves replaced in 2 years.

And, the alternative of Republicans controlling all three branches of government would be good how?

I wasn't implying that republicans controlling all three branches of government would be good. In fact, it's rather horrifying considering the current state of that party.

However, even if democrats won back the majority of congress -- are there enough left leaning democrats enough to support Bernie's platform?