Not all the Dems are spittle flying Air America type radicals. A bunch of them are still somewhat reasonable, and some are even comparable to 'moderate Republicans'. 'What happens' largely depends on how extreme Hillary gets during the first term.
Some kind of 'socialized medicine' 'single payer' (or whatever you want to call it) health insurance scheme attempt is inevitable. I think a majority of Americans favor 'universal health care' and would welcome a 'plan' where everyone is covered. It seems to me that employers currently pay most of the health premiums in this country and would jump at a chance to transfer the burden to someone else.
So if she has a majority of both Americans and employers on her side, she's there.
On national defense, who knows? I don't think she's a '60's 'all we are saying is give peace a chance' hippie (anymore), would retaliate immediately if we are attacked. OTOH, she wouldn't get entangled in 'preemptive' wars, either and the Dem congress wouldn't allow it.
On taxes, well you know where that's goin'. The upper 1%-15%...and corporations will get hit hardest. Nevermind that corporations don't pay taxes, they just add it onto the price and pass it along to you and me.
Gun control? That's been a loser for the Dems but there are still enough gun grabbing blissninnies in Congress to force something-maybe another AWB.
The size of fed.gov (Thanks Bush

) won't decrease under a Hillary admin but hopefully she'd address illegal immigration in some other way than amnesty. The next POTUS will have to deal with illegal immigration, the elephant in the living room is too big to ignore.
AND, I think it's likely the Dems will be sharply divided whichever way she goes-'semi' moderate or hard left. So they'll schism like the Republicans, with lots of infighting.