Indeed, a united front might cause the Democrats to cave, and obviate the need for a shutdown. Republicans in Congress should also realize that they will inevitably receive much of the “blame” in the event of a shutdown, no matter how they feel about it. So why not embrace it? If (and when) the strategy works, they can share the credit.
Voters—the people who put those timorous Republicans in office in the first place—expect progress towards conservative goals, not consistent surrender to Democratic obstructionism. The GOP-controlled Congress already failed to repeal Obamacare and fumbled tax reform. Standing firm on the border wall would go far toward restoring Republicans’ confidence and self-respect.