It depends on the specific toilet you select. All toilets are designed to have at least a little room behind the tank to the wall when installed on the specified rough-in. One of the highly regarded toilets here (I put two in my mother's house) is the Toto Drake. This normally has about 1-1/8" behind it, so it would just fit in your situation. Those I have in my house (also Toto models) only have 3/4" behind them, so they would NOT fit. You need to look at the specification sheets, but I do think you'd like the Drake, if you should choose that.