Trying to set SRID for a Geometry

I imported precinct data from the Harvard Dataverse into Postgres 9.3 using the PostGIS Shapefile Import/Export Manager.

It creates a geom column with a SRID of 0. I think the data is projected as SRID 4326 as I was able to view a map of it using TileMill when I chose WGS 84. However, QGis says it is EPSG:4019 so maybe that is the problem.

How can I import it with this SRID? When I try to change the SRID it fails.

SELECT UpdateGeometrySRID('public', 'precinct', 'geom', 4326);
ERROR:  Geometry has Z dimension but column does not