Phage predation is an important factor for controlling the bacterial biomass. At face value, dense microbial habitats are expected to be vulnerable to phage epidemics due to the abundance of fresh hosts immediately next to any infected bacteria. Despite this, the bacterial microcolony is a common habitat for bacteria in nature. Here, we experimentally quantify the fate of microcolonies of Escherichia coli exposed to virulent phage T4. It has been proposed that the outer bacterial layers of the colony will shield the inner layers from the phage invasion and thereby constrain the phage to the colony's surface. We develop a dynamical model that incorporates this shielding mechanism and fit the results with experimental measurements to extract important phage-bacteria interaction parameters. The analysis suggests that, while the shielding mechanism delays phage attack, T4 phage are able to diffuse so deep into the dense bacterial environment that colony-level survival of the bacterial community is challenged.