If you started from the pilot hole with the step but, you've probably work hardened the area around the bit. If it's a cheap bit (Harbor Freight/TiNi coated) then it could also be the bit. I use cobalt bits anytime I'm drilling into stainless steel. I have a couple (smaller bits) that are too dull to cut into it now. Luckily I don't use those too often.
You need enough coolant/lubricant to both keep the bit, material you're drilling through, cool and lubricated to do the job. Just using a little probably isn't anywhere near enough.
Try drilling one step, then cooling down with water from the hose. Make it cool to the touch again before going to the next step. If you can, you might want to have a slow stream of water going over the bit and work area too. That can be tricky if you're working alone.
IMO, drill bits is one of the tools you don't want to go cheap on. Sure, you could make a couple of holes with the cheap bits, but then you're out buying new ones for the next time you need to use them. Getting good bits means you'll get many more holes from them. The cobalt bits I've been using easily last 3-4x what the TiNi coated bits did. Cool the material/bits decently and they last even longer.