The Democrats cannot reopen the government without either the consent of the GOP majority in the Senate, and/or the GOP president. Those two actors are refusing to do so. The onus is indisputably on them.
Moreover, the Democrats have only been in control of the House for 12 days. For two years the GOP controlled both houses of Congress and the presidency and could have funded the wall without any Democratic support at all. If the wall was so important, why did they not push it through then?
I agree that there is bloat, waste, and abuse in the government, but often not of the kind that gets attacked. (cf: The Pentagon.) I don’t believe it is realistic to say to federal employees who have been caught up in this pointless and avoidable shutdown that they should just find other work.