When a texture is on fractional coordinates, the GPU needs to use smoothing to try to calculate the appropriate colors of pixels. This can cause clipping or blurring. A simple solution is to use Math.round() or something like that to round to the nearest integer when positioning the TextField.
Remember, though, if the parent (or the parent's parent, etc.) is also positioned on fractional coordinates, that is also going to cause the same issue.
I came up with this solution for rounding the position of text to the nearest pixel in global coordinates (to account for the parent and parent's parent, etc.):
var matrix:Matrix = textField.getTransformationMatrix(stage);
textField.x = Math.round(matrix.tx) - matrix.tx;
textField.y = Math.round(matrix.ty) - matrix.ty;
It may be overkill in many situations, but I'm including it here for anyone who might find it useful.