[I would also challenge the Dems to engage as well. Don't be the party of obstruction.]
It seems to me that you are functioning under a belief that Democrats are objecting on political reasons.  Your idea of "engagement" for Democrats to entertain the repeal of Obamacare regardless of objection or issue to policy or process?
The Democrats are just supposed to ignore the compromises already included, such as the compromise from the initial hope for a universal or a single payer system for a universal insurance plan created by a conservative think tank.
Nor would they have a valid objection to the closed door secret no public/committee process straight to the Senate floor approach McConnell is pushing?  Or that Obama often tried to meet Republicans half-way (even going to a Republican retreat to answer questions) and engage them in the process that Trump has yet to even loosely resemble?  And no, threatening Republicans with "I'll go to the Democrats" isn't engaging Democrats.