His base doesn't matter. They aren't going anywhere and cannot be shifted. Many millions of people who voted for him in 2016 were never part of his base to begin with, they just voted along party lines or in opposition to Hillary, or in some cases, wanting to burn it all down.
Drag it out. Democrats can propose bill after bill that solely restores pay cheques to employees, and the Republican Senate and/or the Republican President can shoot them down. Or accept them. Either way works for the Democrats.
Once the President starts paying his employees - something he is noted for not doing - negotiations can begin in earnest.