The problem isn’t so much Democrats as some Republicans. We all know where the Democrats stand on the various issues. We have a GOP majority in the senate, but a number of GOP senators oppose eliminating the fillibuster. I suspect they secretly share more in common with Democrats than conservatives, so the fillibuster is—in their minds—something that can both give them political cover in the GOP as well as prevent conservatives from having a say.
We also need to consider what happens the next time the Dems have the majorities and the President.