They can, and they do. The Usual Suspects have been running on "these gol'durned activist judges!!!1!!" for 30 years. Then they
immediately plunged into their own radical judicial activism as soon as they had the keys. They are originalist when it suits them and activist when it suits them. And although they are hypocritical, at the end of the day they're doing exactly what Louis Brandeis said a SCOTUS justice not only should but can't avoid doing. So for Scalia and his henchmen, bad process but good (for them and weirdly, by the principle that elections have consequences, us) result.
As with science or economics, 99% of the people who yell about the law are 99% ignorant and can easily be whipped into a frenzy. By the goose/gander principle, it was inevitable that this strategy would boomerang against Movement Conservatism. The reaction that buries them is going to be every bit as idiotic and dishonest as the flag-waving, genuflecting in favor of them was.