3’ diameter drain is a minimum required to handle a toilet and sufficient for a full bathroom (for gravity systems). You other option would be to use low profile "Up-Flush" sewage lift pump system (example: http://www.accentshopping.com/product.asp?P_ID=150032#tabtop).
It supports two additional connections like sink and a shower / tub and uses 2” diameter discharge pipe.
There might be a problem with 2x6 framing of your wall. If this is a bearing or exterior wall you can only drill a hole in the stud up to 40% of its width (no closer than 5/8” to the face of stud) or notch 25% of it. 60% boring is permitted on bearing walls only if you double the stud and you cannot go through more than 2 doubled parallel studs. For non-bearing walls, 40% notch and 60% boring is OK for the entire wall.
With 2” diameter pipe bearing / exterior wall wouldn’t be an issue.
For 3” or larger gravity drain you need minimum slope of 1/8” per foot. Don’t forget venting of this system and make sure you always check your local code requirements.