ACTUALLY.... 2 options come to mind:
1) Get a rug gripper thingy (you'd need one if you got a rug anyway), and put down a big *blanket* on the floor. Then, easy, easy the blanket gets tossed in the wash. These used to be really common. In fact, they were called 'floor blankets', or 'baby floor blankets'. They were 5x5 or 8x10. It's what mom's used before playpens took off. I remember as a kid that EVERYONE had rules that you had to stay "on the blanket". First "listening" practice. Typically by 9mo babies would even do crawling laps around the edges, or be sitting on the edges with their arms up calling, because from a few months onward parents just directed their rollers and crawlers to stay on the blankets.
(Huh. You know, I'd completely forgotten about those things. I remember ours. It had lions on it. It was common for them to have big patterns on them; to hide spills, but to be on a white background so you'd know when to toss it in the wash.)
2) Get a rug, and do what people in the middle east have done with their persian rugs for centuries (and what I still do with mine). Take them outside, hose them down, use a scrub brush and soap to scrub them clean, hose them off. ((Granted, people in the middle east usually use buckets of water instead of hoses)). Then you just hang it up to dry.