Socially, no. Fiscally, no. Militarily or diplomatically, no. Environmentally, no. In terms of commercial regulations, no.
the left has a predictable, transparent trend of lionizing dead/retired Republicans to lament the current lot
I get the thrust of the question, but Obama is a Democrat because he chose to be, and he acts according to the context he finds himself in. If he had an R next to his name, he'd be advocating tax cuts for the wealthy, the abolition of public schools and so on. If Reagan was alive and running for president today and kept his loyalty to the Republican party, he'd be saying all the same crap Romney's saying. They have some influence (more than most), but they don't define what a Democrat or a Republican is. They are confined by the desires of the party platforms, current events, and the political atmosphere. It's helpful to point out that the Republicans are much more small-government and free-market now than they were in the '80s. But, Obama and Romney themselves are mostly just executors of the party will.
Here is a question, what would Republican party look like 30 years from now. The Republican party of 1980 is totally different than the Republican party of today. Democrat party have changed, but not to nearly the extend of the Republican party.