You need a toilet auger, there made to snake toilets.
Hey, the past day or two the toilet was clogged after a large ... but, I digress. It's been able to go down since however, it is slower than it used to. We've tried plunging with different plungers, using vinegar and baking soda, and clorox a couple times each. Someone, does not want to use the snake which I think it might help but this person in the house (who shall remain anonymous) doesn't want to thinking it won't work and it takes too much.
It's common to see toilet paper getting snagged on a sharp edge of the toilet flange. Somebody also could have flushed a toothbrush or a Q-tip and no amount of clorox will clear that. I would remove the toilet, inspect the flange and check for debris. If it passes this test, then it will be much easier to snake the drain with the toilet removed.
If I pulled the toilet every time I was called out on a toilet stoppage, before trying to clear it with a plunger and auger I wouldn't have many repeat customers. Pulling the toilet is the last option.
you can try to flush a bio diaper or a small bio wash cloth other than that you are stuck with the auger.
We use a closet auger with the large 1-3/8" end on it.
Smaller cables can go right by the obstruction and not move it.
I wouldn't try flushing more wash clothes down like Cameron suggests. I think he's just messing with you.