Are you looking for a manufacturer who would license your design and take over sales and distribution? Or a contract manufacturer who will make them for you to sell?
Licensing it is probably going to be hard, you have to find someone who wants it, and into whose line it fits, and you have to be realistic about what a fair royalty percentage is (in this industry it's a single digit number, and you can almost certainly count to it on one of Bart Simpson's hands with a couple fingers to spare). Finding someone to make them for you, provided you are realistic about what that costs, is not too hard.
There is very little volume furniture manufacturing in the US at the moment, but by "volume" I mean thousands of pieces a month. But if you need that kind of volume, you're probably not asking questions like this here. Smaller volumes, or high volume products with little labor input (mostly CNC cut, minimal assembly) can be done in the US.