So, how much damage do you think Trump will be able to do? Considering he's at loggerheads with much of the GOP, I'm cautiously optimistic.
They'll all kiss the ring, as will a good chunk of the Democrats.
Assuming that happens, what can be done to counter it? Let's think proactively.
I was being a bit hyperbolic. For one, it's very likely that the filibuster will remain in place, which will mean that on many issues, if the Democrats can present a united front (or even just near-united), they can block most legislative action, along with things like Supreme Court and Cabinet appointments. Sen. Graham has already said he'd vote against killing the filibuster, and there's a good chance that some others, like Sen. Collins, would join him.
For another, there are some Republicans who may well buck the party--people like Sen. Collins, from Democratic-leaning states, or people who will do so on principle, like Sen. Graham with the filibuster or Sen. Paul with certain Cabinet appoinments (he's said he'd block any attempt to appoint Bolton or Giuliani as Secretary of State, because they're massive hawks and he's a non-interventionist).
Probably the single most important--and achievable--thing they can do in the short term is pour resources into the Louisiana Senate runoff. If they can win that--and it would be an uphill battle--then they'd only need 2 Republican Senators to block any legislation, which is significantly more attainable than three, especially when you know that on many issues you'll already be able to find at least one who's said he or she will oppose it. It won't always work--executive orders, lower federal courts, reconciliation--and they won't be able to get anything of their own through (since they're nowhere close to having the House), but that's how I'd try to stem the tide.