Cohorts of 3-6 patients receive escalating doses of recombinant vaccinia-MUC-1 and recombinant vaccinia-TRICOM vaccine until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 2 of 3 or 2 of 6 patients experience dose-limiting toxicity. Once the MTD is determined, an additional 10 patients (including 5 HLA-A2-positive patients) receive vaccination as above at the MTD and sargramostim (GM-CSF) subcutaneously on days 1-4 and 29-32.