My Big Boy tomato plant is bushy and huge, but I have no tomato blossoms. It's the first week of May and nothing. Did I use too much fertilizer or what?
You probably had too much nitrogen in the soil during the first stage of growth -- because one effect of this is the plant may not ever set fruit.
That's why the general advice for fertilizing tomatoes is to apply tomato fertilizer when planting and then wait until golf ball-sized fruits are present before resuming a fertilizing program.
I'd suggest pruning back excess leaves and stop fertilizing the plants. You can also try adding bone meal or granite dust to the soil, because these have no nitrogen and are high in phosphorous which can encourage fruiting.