All four feet of an elliptical machine need to be level or you're going to find that your machine wobbles back and forth when you're working out. Whether or not you can make your elliptical more sturdy on carpet depends on the type of carpet. If you have thin carpet, you can make adjustments that will likely improve the elliptical's sturdiness. If you have plush or shag carpet, however, you won't be able to prevent it from wobbling and should look to move your machine to another location.
If your elliptical isn’t sturdy on your thin carpet, you may be able to improve the situation by adjusting the feet on the machine or by using a mat or piece of plywood. Most ellipticals feature feet that you can raise or lower by twisting them individually. If your floor surface is uneven, adjusting the height of one or more of the feet could fix the problem. A thin mat or a piece of plywood between your machine and carpet could also help level the floor surface.