They claimed Trump couldn't appoint Gorsuch while Trump was being investigated via the Russia hoax too, and look how that turned out. Appointing justices is a Donald & Mitch show, no House Dems need apply.
As I noted in another thread, while the Dems were gnashing their way through the "impeachment," the Senate approved 11 more of Trump's nominees for federal judgeships. McConnell's motto is "Leave no vacancy behind." He and Trump intend to fill all of them by end of Trump's first term...and any SCOTUS vacancies as well.