Only the initial size matters, tiled background will just copy paste the object as you stretch it. But if you are using sprite and stretching it that can make some problem's.
Making the initial size of the object smaller will always improve performance, also making the tiled background size on power of 2( 4,8,16,32,64,128,256 etc) size will make it even more efficient, so if you have some lag ussies try setting the size to 256 then 128 and compare the difference.