If you think about it for a second, you will realise that this isn't the case.
Think of pixels as boxes. If you have a 3x3 box in a 37" screen, and a 3x3 box in another, 60" screen, are the boxes bigger on the 60" screen?
EDIT: you asked if the 60" have a max res of 1920x1080, generally nowadays the medium-higher end 46"+ have that resolution. But you should be checking the specifications of the particular unit as well.
Not necessarily. The physical size of the pixels depends on both the resolution (length x height ex. 1920x1080) and the diagonal measure of the screen. If there are 3 million pixels on a 13inch display to produce 1080p (1920x1080) and 3 million pixels on a 70 inch plasma to produce 1080p, it makes sense that they would have to be much smaller to fit on the smaller screen. Pixels are generally smaller on computer screens because it makes for sharp text, and generally much larger on TVs because they are viewed from farther distances.