There are more Government workers who are Democrats than Republican. The shut down is already causing political pressure for the Democrats, via threats from union leaders, who give most of the union donations to Democrats; 90%.
If the Union leaders decide to have a strike, to gain control of the situation, this will open the door for Trump get rid of the unions, with scabs. President Reagan did this with aircraft controllers. This will hit the Democrats where is hurts; donation wallet. Donation money will need to go to striking union members.
The wall is needed because it is a passive restraint to illegal immigration. Sealing the border with troops is dynamic and more expensive. The latter is also subject to the whims of who is in charge, and can be dissolved easier than a wall, by Executive order. A wall is more permanent and can outlast changes in power in Washington.
Shutting down the border can be an effective tool in terms of concessions with Mexico. We have a huge trade deficit with Mexico that costs more per year, that a one time wall cost. Border sealing will cause business pressure on the government of Mexico. Mexico may choose to compromise and pay for a southern border wall along its central American border. This will take the pressure off the US border. A wall will then be very effective and may be the only way the Democrats can keep union due coming their way.