Sad as I am to see it go, the answer has to be “not very.” It certainly couldn’t withstand much pressure.
For better or for worse, the legislative filibuster has survived the most vehement of partisan rancor. Its judicial cousin, by contrast, has tended to fold at the first hurdle. In 2003, when Chuck Shumer began filibustering Bush’s nominees to the lower courts — a departure that tested what was a relatively new “norm” — the GOP came close to getting rid of it. In 2013, after the GOP had successfully filibustered 5 — yes, just 5 — of Obama’s non-SCOTUS judicial picks, Senator Reid did what the Republicans had not a decade earlier and killed it stone dead (with a carve out for the Supreme Court). And now, just minutes after the first ever partisan filibuster of a SCOTUS nominee, Mitch McConnell has nixed it completely.
It doesn’t take much searching to conclude that, as a “norm” or “system” or “political institution,” there wasn’t much there after all.