I'm not old enough to remember it, but the conventional wisdom now seems to be that the Reagan White House got caught flat-footed, and offered up an at-best poor defense of and campaign on behalf of Bork.
Plus, now there are many alternative sources of news. The mainstream media does not dominate like it used to, so it would be harder to demonize a Scalia/Thomas type. It would be attempted, no doubt, and would succeed to an extent, but now we at least have some more weapons to fight back with.
And of course the GOP has a majority in the Senate. At least two of the GOP members of the Gang of 14 have said they would vote to pull the nuclear/constitutional trigger if their Dem counterparts deemed a candidate 'extraordinary' for ideological reasons. If a full Senate vote can be forced, then the chances are good as Bush could afford 5 defections.
It may be close. We might lose. But you never know until you try.
And unless the wretched theory of the "Living Constitution", which grants near-absolute power to the Sup Court, is thoroughly debunked and then rejected by the people, then it will never be eliminated, or even relegated to irrelevancy.