There is no way I know of that you can make a rug on a regular sewing machine. A regular machine won't handle the thickness. However there are a couple of options you can use to cover your floor.

The site at the bottom is how to make a floor cloth. There are plenty more sites on line if you google how to make a floor cloth.

Floor cloths have been around for centuries. The pioneers used them to cover their floors and add a decorative touch to their rooms. They are made from canvas, painted and then sealed. I would suggest you start with artists preprimed canvas. You can buy it at most art supply stores or probably on line. It has the gesso coat already on it so it is ready to paint and well worth buying rather than canvas and gesso.

As for pattern to paint you can take that off of anything even fabric. lay tracing paper on top and trace and then transfer on to the floor cloth with graphite paper.

Use the liquitex paint to paint and then seal it. Use a foam backing to keep it from slipping.

If you don't want to do this then take a paper template of your potential rug in to a carpet place and buy a remnant. Have them cut it to size and bind it. It will need a non-slip underpadding too.

Here is a link that might be useful: floor cloth

I think I read on Tipnut or somewhere about how to make a floor rug out of old towels. The gist of it was to take the old towel fold it and stitch borders of fabric around it to make it look better than an old towel on the flooor. LOL. A any rate the towels/rugs looked really good and they would be washable. As oilpainter said, you would need a non-slip padding underneath. Do a search on google on recycling old towels and see what you can come up with. If I find the link, I will post the link back here.
Murphy

Murphy:

What a great idea to use toweling. If you put a stiff interfacing in between 2 layers it wouldn't be so floppy. Yet it would still be washable and 2 layers would be softer to stand on. I think if it's an odd shape though I'd buy towling instead of using towels. You'd eliminate the borders. I'll have a google too, to see if I can find that site. This sounds interesting. It would be great for a bath mat too.

Terry towels is what came to my mind in the beginning but I couldn't figure out how to make it look decent. I even thought of cutting up some towels and piecing differents squares of color. Never thought of bordering it with fabric...if it was the correct fabric, it would make it look better and lay better. I never thought of buying terry fabric...duh!! Thanks for your brainstorming for me. I will search the internet.

http://thenewnew.blogspot.com/2008/09/recycled-bath-mat.html

This is the link I found. Putting a pretty fabric border on it looks really good. Oilpainter, great idea about the interfacing. Or you could use as many layers of towelling that your machine could handle.
And the best thing for me is to use up those old towels I have around. No "old" towels, just use what you have and have an excuse to buy new ones...change your decor. After all they are going to be on the floor and no one will look at them closely enough to know that they are old towels.
Murphy

Check the site out, may put this on my bucket list.

Here is a link that might be useful: Rug made with Neckties.

I have made a number of rugs over the years. I have crocheted strips of cloth or you can make a braided rug. I just finished a little rug for a spare room that I made like a rag quilt using flannel scraps leftover from a flannel quilt I had made for the bed in the room. If any of these ideas sound like what you want just Google crocheted rugs, braided rugs or rag quilts and you might come up with an idea. There is a type of non slip stuff you can buy by the roll to put under rugs to keep them from slipping.

Just thinking outloud here.

What about getting some carpet remnants, a really sharp Stanley knife, carpet tape and measuring tape. Draw out the measurements of the area you want the rug to occupy and design something--a few borders, a center square or rectangle. Use Google image search for ideas.

Using the design as a pattern--cut out the carpet remnants, use the carpet tape to insert the center square (or whatever) and secure.

It doesn't cost a fortune to have a small rug bound--most carpet stores offer this option.

Here is a link that might be useful: Like decribed here

Thanks so much for the ideas. I thought of crocheting or rag rugs but the way I want it to be is straight in front of the sink and then angled on both sides...to the pullout trash on one side and the dishwaher on the other. I am not good enough to come up with the pattern for the angles etc. And, I thought of cutting carpet. I have remnants from moves, but then it wouldn't be washable. Thats a great idea for someplace else though and I am thinking where I can use those. I am very interested in the "towel rug" and am going to use fabric to coordinate with other things in the rooms...maybe the valances I am going to make or black and white checked tablecloth....I have a lot of ideas now. The possibilites are endless, huh? Sounds fun.

I have crocheted rag rugs for my kitchen.. and now I am making a hooked rug with bright color fleece strips.. it is really pretty.. bright greens, pinks, oranges, and blues.. just cut your stips of left over fleece and use the fleece like a piece of rug yarn.. and hook it.. looks pretty neat.. I also used a rotary cutter with a scalloped edge on it .. and that gave it some interest..

Go buy a box of carpet squares in the color and pattern of choice. They fit together and can be cut to size. Get enough to have leftovers as you can replace the squares when they get too stained to clean. You can get some butcher paper and cut a pattern to help with the shape problem. Just lay the paper on the floor and trim to the shape you want. It doesn't have to be exact (close but not exact) Lay your squares on the pattern the way you want them and cut to fit. Most of these squares can be cut with a good pair of scissors.

you could make a rug the same way a snuggles is made. there washable. its like makeing a quilt but using towel's or old hoodies,or blanket's for batting.

You all are amazing. What neat ideas. Chickadee, I bet your rugs are so pretty. And, huggybear, I never thought of a hooked rug, though I think my "hooker" tool :-) got sent to goodwill in our last move. But, is the backing that you have to use washable? Pris - I have made that pattern out of some brown shipping paper that I had. I never would have thought of carpet squares. Not washable , but like you said, they are cheap and could be changed out. I guess you would just use carpet tape to put them all together? Chrzty, I am not familiar with what snuggles are. Thanks all of you for your great brainstorming. Great ideas !