1. An apparatus, comprising: at least one processor; and program code configured upon execution by the at least one processor to load balance in a computing environment of the type including a plurality of fabrics coupling a plurality of hosts to one or more storage systems, each fabric among the plurality of fabrics coupling one or more of the plurality of hosts to one or more of the one or more storage systems, the program code configured to: determine a fabric limit for a limited fabric resource of each of the plurality of fabrics, wherein the limited fabric resource for each respective fabric among the plurality of fabrics relates to a relative load and/or capacity of the respective fabric, and wherein the fabric limit is an active login limit, an active discovery limit, a zone limit, or a host limit; determine an overcommitted fabric capacity for each of the plurality of fabrics from the fabric limits; determine an allocation of the limited fabric resource for each of the plurality of fabrics; and balance utilization of the limited fabric resource across the plurality of fabrics based at least in part upon the determined fabric limits and determined allocations of the limited fabric resource for the plurality of fabrics, wherein the program code is configured to balance utilization of the limited fabric resource by migrating at least one virtual machine that is resident on a first host among the plurality of hosts and that utilizes a first fabric among the plurality of fabrics to use a second fabric among the plurality of fabrics, wherein the at least one virtual machine that is migrated to use the second fabric remains resident on the first host after migration, wherein the program code is configured to balance utilization of the limited fabric resource across the plurality of fabrics based at least in part on the determined overcommitted fabric capacity for each of the plurality of fabrics, and wherein the program code is configured to migrate at least one virtual machine by, for a first virtual machine: powering down the first virtual machine; reconfiguring the first virtual machine to utilize the second fabric instead of the first fabric; and powering up the first virtual machine such that the first virtual machine utilizes the second fabric instead of the first fabric.